CDC's own disclaimer on their combined Covid-19+Pneumonia dataset, which is frankly more relevant than merely the pneumonia one:
Data during this period are incomplete because of the lag in time between when the death occurred and when the death certificate is completed, submitted to NCHS and processed for reporting purposes. This delay can range from 1 week to 8 weeks or more, depending on the jurisdiction, age, and cause of death. [...]
COVID-19 death counts shown here may differ from other published sources, as data currently are lagged by an average of 1–2 weeks. [...]
estimates of completeness for pneumonia deaths may provide context for understanding the lag in reporting for COVID-19 deaths, as it is anticipated that these causes would have similar delays in reporting, processing, and coding. However, it is possible that reporting of COVID-19 mortality may be slower or faster than for other causes of death, and that the delay may change over time. Analyses to better understand and quantify reporting delays for COVID-19 deaths and related causes are underway.
And yeah, there are only 2,214 Covid-19 deaths reported by that CDC dataset

Whereas on Apr 06, 2020:
the United States as a whole had reached a death toll of more than 10,000, according to the coronavirus resource centre at Johns Hopkins University in Maryland. The U.S. has seen 10,335 die from COVID-19 causes, according to the [JHU] tally.
So why would you expect the CDC pneumonia stats to be more up-to-date... especially since... the CDC guidance for how to record the cause of death has also evolved:
To try and get a more accurate picture of the crisis, the CDC last week issued updated guidance for certifying deaths due to COVID-19 – protocols similar to those in place for pneumonia and influenza. According to the new directions, if a patient has died from pneumonia, for example, but was also tested positive for COVID-19, someone is required to specify whether COVID-19 played a role in the death and whether it was actually the underlying, primary cause of death.
Cécile Viboud, a staff scientist at the National Institutes of Health (NIH) who specializes in the mortality associated with infectious diseases, said it will likely take years to know the actual death toll of the contagion that has nearly paralyzed much of the nation.
In previous research on the 2009 H1N1 pandemic, Viboud said she concluded that only 15% of the deaths attributed to the disease were identified in laboratory testing.
Instead of trying to suss under which heading the extras deaths might have been recorded, a simpler heuristic [for now] would be to look at the total causes of death and look for a spike; see related/similar question here on Europe and their EuroMOMO metric, where a spike did show up after some weeks, precisely in the regions hit most by Covid-19, debunking similar conspiracy theories that there were no extra deaths in Europe due to Covid-19.
I have qualms about the mod leaving this question open, while it's clearly an "unresolved current event" to a good extent, but there you have the official disclaimer(s) for the [CDC] data.
Excuse my squiggles below, but besides the fact that incomplete data precludes a serious analysis, what exactly is the claim "fallen off a cliff" in the Reddit image referring to here? That:
- 2019-20 is below the other years on one or both of the big oval areas? (More "suspicious" in the 2nd black one?)
- 2019-20 has a different post-peak downward slope than the other years? (Pink arrow)
- 2019-20 has a substantially different slope just for the last segment/data point (green circle)?

Assuming we had the final data in, which of these claim are we supposed to address?
If the claim is (per discussion on chat) "the graph looks suspicious", then probably the best rebuttal is applying the exact same (faulty) graphic method to previous years' (incomplete) data, truncated up to March, as was reported back then.
This was done by a Twitter user, but he links to the CDC data sources, so hopefully/presumably it's verifiable by others (there aren't any calculations/statics involved, just plotting):

Credit should go to @CL for finding this.