Yes, under the current rules and best available projections from US Federal government.
Social Security Administration's own projections from SSA's Office of the Chief Actuary:
Scheduled and Payable Benefits
Scheduled Benefits are those that current law promises. Payable Benefits are those that projected Trust Fund balances can finance. Payable benefits are an across the board reduction from Scheduled Benefits in a given year starting with the Trust Fund exhaustion in 2036, therefore Payable Benefits and Scheduled Benefits are the same in 2030. The SSA Actuaries estimate that the across the board reduction under a Payable baseline will be 21.8 percent in 2050 and 23.2 percent in 2070. These reductions would apply to the final benefit amounts, not the average indexed monthly earnings (AIME) or the primary insurance amount (PIA). Both the Scheduled Benefits tables and the Payable Benefits tables compare the respective baseline to a policy option built on top of Scheduled Benefits
As of 2013, CBO (Congressional Budget Office) projects that revenues will consistently lag outlays: http://www.cbo.gov/publication/44972
CBO projects that under current law, the DI trust fund will be exhausted in fiscal year 2017, and the OASI trust fund will be exhausted in 2033.
If a trust fund’s balance fell to zero and current revenues were insufficient to cover the benefits specified in law, the Social Security Administration would no longer have legal authority to pay full benefits when they were due.
In 1994, legislation redirected revenues from the OASI trust fund to prevent the imminent exhaustion of the DI trust fund. In part because of that experience, it is a common analytical convention to consider the DI and OASI trust funds as combined. Thus, CBO projects, if some future legislation shifted resources from the OASI trust fund to the DI trust fund, the combined OASDI trust funds would be exhausted in 2031.
The full publication has methodology and the data tables.
To further help illustrate the "headed" part, here is the projected SS Trust Fund reserve depletion years over 1985-2014 years from Social Security Adminitration "2014 OASDI Trustees Report" (Table VI.B1.—Long-Range OASDI Actuarial Balances and Trust Fund Reserve Depletion Dates as Shown in the Trustees Reports for 1982-2014, Page 159).
I plotted the years as well as the trendline in Excel based on the last column in that table.
I dropped 1982-1984, since 1982 projected 1983 insolvency while 1983-84 projected no insolvency at all; so the chart would go to +infinity if these were included.