My TL;DR summary is: there is too much uncertainty at this stage to know what the specific effect of an ACA repeal would be.
The rest of this answer explains in more detail that:
On the effect of health care reform and expanded coverage on mortality rates,
- Two studies involving four states that increased insurance coverage found that states that enact health care reform see a relative decrease in mortality rate compared to control states with similar economic and demographic conditions that do not enact health care reform. (See , ).
- One study found that in a state that expanded Medicaid, there was no significant effect on measures of blood pressure, cholesterol, or glycated hemoglobin , however, this study did not look at mortality rate, and also had a much smaller sample size than the others.
- On a nationwide level, the mortality rate among the uninsured was greater than among the insured, even after controlling for many potential confounding variables (age, income, health, etc.) .
Multiple sources claim that upwards of 20 million people could lose insurance if the ACA is repealed, with the specific number depending on the mechanism of the repeal and the reactions of the insurance market (this assuming no replacement - it is impossible to say what the effect would be of a replacement whose details have not been revealed, as of now). These estimates are based on
- the number of people enrolled in the individual exchanges (12 million under age 65 in 2016, 10 million of which are subsidized ),
- the number of people who gained Medicaid eligibility as a result of the ACA (11 million under age 65 in 2016 ),
- the number of people insured through the ACA that are expected to gain insurance through another means if it is repealed, and
- the effect of an ACA repeal on the nongroup insurance market (including nongroup plans purchased outside of the individual exchanges, which cover 9 million people under age 65 as of 2016 ).
Items (3) and (4) are predictions of the effect of repeal on a very complex and sensitive system, and so have quite a bit of uncertainty. (See , and , .)
Sanders shared this ThinkProgress piece on his Facebook page on January 5, 2017; it appears to be the source of his claim.
That article claims:
Nearly 36,000 people could die every year, year after year, if the incoming president signs legislation repealing the Affordable Care Act.
which is already less certain than the Sanders tweet (which says 36,000 will die).
They compute the 36k number based on:
They then compute the 36,000 number as: 29.8 million no longer insured/830 insured corresponds to one death prevented.
This is a problematic calculation, because the 29.8 million number includes children, while the 830 number is for adults insured. But that aside, how credible are those numbers?
First, let's look at the effect of health care reform on mortality.
The only nationwide study that I have seen is a 2009 study  that looked at the mortality rates among the insured and uninsured. At the individual level, it tells us the increased risk of mortality that is attributed to lack of insurance:
After [age and gender adjustments and] additional adjustment for race/ethnicity, income, education, self- and physician-rated health status, body mass index, leisure exercise, smoking, and regular alcohol use, the uninsured were more likely to die (hazard ratio = 1.40; 95% CI = 1.06, 1.84) than those with insurance.
And at the population level, it estimates:
approximately 44,789 deaths among Americans aged 18 to 64 years in 2005 associated with lack of health insurance.
This is not to suggest that repealing the ACA would bring about that many deaths; the reduction in number of uninsured US adults due to the ACA is not equal to the total number of uninsured adults in 2005. But, at the population level this suggests a ballpark number of approximately 1.2 deaths per thousand uninsured adults per year attributed to uninsurance. (44789 deaths in 2005 among 18-64 year olds attributed by the study to lack of insurance, divided by the 36.864 million adults aged 18-64 who were uninsured in 2005.)
For comparison, the article Sanders was referring to (which uses risk estimated by a different study, not the study we have just discussed) assumes there will be about 1.25 (36000/28900) deaths per thousand uninsured per year.
Other studies on the effect of increasing health insurance coverage and other health care reforms suggest this varies tremendously by state:
830 adults gaining health insurance prevents 1 death per year, according to the study in Massachusetts , as quoted above. This is the estimated risk the ThinkProgress article uses in its analysis.
According to another study that compared states expanding Medicaid coverage (NY, AZ, and ME) and states that didn't ,
176 additional adults would need to be covered by Medicaid in order to prevent 1 death per year
This study found a much greater benefit of expanded Medicaid in reducing mortality, compared to the one the ThinkProgress piece cites (i.e. using this number, they could have arrived at a much higher estimate of deaths).
A study on expanded coverage in Oregon  did not look at mortality, but did look at other measures of health, and found no significant benefit to increasing Medicaid coverage. This is obviously a much smaller (i.e. no) benefit of expanded Medicaid in reducing mortality, compared to the study the ThinkProgress piece uses.
Not only is there wide variation across these in terms of benefits of expanded insurance coverage, the authors of all these studies caution that "results may not generalize to other states"  (and identify specific variables in the states under consideration that could cause the benefits to be greater than or less than other states). For example, expanding health insurance coverage in a state where most of the previously uninsured do not have doctors or hospitals nearby, will not have the same effect as expanding health insurance coverage in a state with a much higher density of healthcare providers. A state with a higher baseline rate of insurance coverage before enacting reform will not see as great an effect on mortality rate after enacting reform . Similarly, the Oregon paper  notes that a small-scale healthcare reform effort is substantially different from a large-scale healthcare reform effort, for better or worse:
the newly insured participants in our study constituted a small share of all uninsured Oregon residents, limiting the system-level effects that insuring them might generate, such as strains on provider capacity or investment in infrastructure.
Next, let's consider the number of people who will lose insurance. This, too, is a subtle and complicated problem involving many variables. The Urban Institute brief claims
a higher rate of uninsurance than before the ACA because of the disruption to the nongroup insurance market.
i.e. it estimates more people will lose insurance than just the individual exchange enrollees or people who gained access to Medicaid as part of the ACA's expanded Medicaid.
Specifically, they estimate that more people will have employer-covered health insurance, fewer will have Medicaid, and fewer will have nongroup coverage:
This is based on the following prediction:
The near “death spiral” in the private nongroup market described earlier is likely to occur immediately after the reconciliation bill’s
provisions take effect. Insurers would recognize the unsustainable financial dynamics of broad-based pooling policies (e.g., guaranteed issue, no preexisting condition exclusions, essential health benefits,
modified community rating) combined with no individual mandate and no financial assistance to spur enrollment. Similar near market collapse has occurred in the past under similar conditions. When New York’s and New Jersey’s state governments implemented community rating and guaranteed issue in their private nongroup markets without also providing for an individual requirement to obtain coverage or financial assistance to make coverage affordable for people with modest incomes, the nongroup
markets unwound (Monheit et al. 2004).
In general, it is plausible - expected, even - that repealing the ACA would not suddenly revert health care back to exactly what it was before it was passed. There have been massive changes throughout the industry as a result of ACA (as alleged both by people who think they have been net positive and people who think they have been net negative, such as this one). However, it's not clear at this point where the dust will settle, so it's hard to say exactly what the effects on insurance coverage and access to healthcare will be.
The U.S. Congressional Budget Office in 2015  arrived at a lower estimate:
CBO and JCT estimate that the number of nonelderly people who are uninsured would increase by about 19 million in 2016; by 22 million or 23 million in 2017, 2018, and 2019; and by about 24 million in all subsequent years through 2025, compared with the number who are projected to be uninsured under the ACA. In most of those years, the number of people
with employment-based coverage would increase by about 8 million, and the number with coverage purchased individually or obtained through Medicaid
would decrease by between 30 million and 32 million.
However, this number should be revised downward because it is based on what was an overestimate by about 8 million of the number of enrollees predicted in individual exchange plans for 2016:
But then potentially revised upward in the case of a repeal through a reconciliation bill that leaves in place market reforms, because in a letter to the Senate Committee on the Budget, they add:
CBO and JCT have not estimated the changes in coverage from leaving in place the ACA’s insurance market reforms while repealing the subsidies and mandate penalties. However, the agencies expect that, relative to the numbers provided above, leaving the market reforms in place would lead to a further reduction in the number of people covered in the nongroup market and an additional increase in the number of uninsured and people with employment-based insurance.
More recently, in January 2017  the CBO estimated that first 18 million, then 27 million, and finally up to 32 million by 2026 would lose insurance (compared to the situation under the current law) if the ACA was repealead via an H.R. 3762-like reconciliation mechanism, leaving the market reforms in place:
The number of people who are uninsured would increase by 18 million in the first new plan year following enactment of the bill. Later, after the
elimination of the ACA’s expansion of Medicaid eligibility and of subsidies for insurance purchased through the ACA marketplaces, that number would increase to 27 million, and then to 32 million in 2026.
based on the following "accounting":
The estimated increase of 32 million people without coverage
in 2026 is the net result of roughly 23 million fewer
with coverage in the nongroup market and 19 million
fewer with coverage under Medicaid, partially offset by
an increase of about 11 million people covered by
mandate penalties and the subsidies while retaining the
market reforms would destabilize the nongroup market,
and the effect would worsen over time. The ACA’s
changes to the rules governing the nongroup health
insurance market work in conjunction with the mandates
and the subsidies to increase participation in the market
and encourage enrollment among people of different ages
and health statuses. But eliminating the penalty for not
having health insurance would reduce enrollment and
raise premiums in the nongroup market. Eliminating
subsidies for insurance purchased through the marketplaces
would have the same effects because it would result
in a large price increase for many people. Not only would
enrollment decline, but the people who would be most
likely to remain enrolled would tend to be less healthy
(and therefore more willing to pay higher premiums).
Thus, average health care costs among the people retaining
coverage would be higher, and insurers would have to
raise premiums in the nongroup market to cover those
higher costs. CBO and JCT expect that enrollment
would continue to drop and premiums would continue
to increase in each subsequent year.
If the market reforms were also repealed, they estimate:
(The number of people without health insurance would be smaller if, in addition to the changes in H.R. 3762, the insurance market reforms mentioned above were also repealed. In that case, the increase in the number of uninsured people would be about 21 million in the year following the elimination of the Medicaid expansion and marketplace subsidies; that figure would rise to about 23 million in 2026.)
The variation in estimates of the potential number that will lose insurance also highlights the danger of drawing firm conclusions. It is extremely difficult to predict the effect of such a complex and far-reaching change. Also, the number of people losing insurance will depend in large part on the mechanism of a repeal, which in turn would affect what individual parts of the ACA (the Medicaid expansion, the market reforms, etc.) stay or go.
The ThinkProgress piece itself notes some uncertainty:
In fairness, 36,000 is a high estimate of the number of deaths that will result if Obamacare is repealed, as there is some uncertainty about how congressional Republicans will repeal the law. Even in the best case scenario, however, a wholesale repeal of Obamacare may cause about 27,000 people to die every year who otherwise would have lived.
but given everything described above, I would similarly challenge their claim that 27,000 deaths is the "best case" scenario.
 Sommers, B.D., Long, S.K. and Baicker, K., 2014. Changes in mortality after Massachusetts health care reform: a quasi-experimental study. Annals of internal medicine, 160(9), pp.585-593.
 Sommers, B.D., Baicker, K. and Epstein, A.M., 2012. Mortality and access to care among adults after state Medicaid expansions. New England Journal of Medicine, 367(11), pp.1025-1034.
 Baicker, K., Taubman, S.L., Allen, H.L., Bernstein, M., Gruber, J.H., Newhouse, J.P., Schneider, E.C., Wright, B.J., Zaslavsky, A.M. and Finkelstein, A.N., 2013. The Oregon experiment—effects of Medicaid on clinical outcomes. New England Journal of Medicine, 368(18), pp.1713-1722.
 Blumberg, L.J., Buettgens, M. and Holahan, J., 2016. Implications of Partial Repeal of the ACA through Reconciliation. Washington, DC: Urban Institute.
 United States Congressional Budget Office, 2015. Budgetary and Economic Effects of Repealing the Affordable Care Act. https://www.cbo.gov/publication/50252
 Wilper, A.P., Woolhandler, S., Lasser, K.E., McCormick, D., Bor, D.H. and Himmelstein, D.U., 2009. Health insurance and mortality in US adults. American journal of public health, 99(12), pp.2289-2295. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2775760/
 United States Congressional Budget Office, 2017. How Repealing Portions of the Affordable Care Act Would Affect Health Insurance Coverage and Premiums. https://www.cbo.gov/publication/52371
 United States Congressional Budget Office, 2016. Federal Subsidies for Health Insurance Coverage for People Under Age 65: 2016 to 2026. https://www.cbo.gov/publication/51385