The simple answer is yes. The social security administration report, which uses conservative estimates, estimates that the trust fund will be running a net cash outflow within about 15-20 years, but there is a large social security treasury, becasue there has been a net cash inflow for so long. It will take until about 2040 - 2050 to bankrupt this cash stash according to the Social Security Administration's report.
Now these are numbers based on the ss administration's report. It seems like every decade the social security adminstration trustees publish a report that says that the social security trust fund will run out, and the date of bankruptcy seems to be about a decade later every time that they release a new estimate.
The time to social security bankruptcy is easily calculated when a number of other factors are known including but not limited to people's future incomes, population size, and population age distrubution. It is comparatively easy to estimate the population size and age distribution in the next few decades, but it is not easy to tell what will happen in the economy in the next 30 years, which is why it is best to use conservative estimates and be safe.
Incomes generally follow productivity, e.g. the more productive an employee is, the more he or she is worth to a company, and the higher his or her salary is. When this happens to the nation as a whole, incomes as a whole rise. Your social security tax is a given percentage of your income, so as people's incomes rise, more dollars go into the social security trust.
Some economists claim that the social security administration's report uses too conservative estimates for productivity, while others point out that inventions like computers that provide a boost in productivity may not come again in the next few decades. Still other economists mention that incomes may decline because foreign workers will do the same jobs as americans better for less money.
To summarize: it is debatable as to whether or not social security will run out in any living person's life time, but if it does, it will not be within the next 25 years by all estimates.