Robert Reich says so, "Why More Immigrants Are An Answer to the Coming Boomer Entitlement Mess", which is also linked to by Mark Thoma. He has been on the Social Security Advisory board and has heard all the tales of coming Demographic Doom due to the impending wave of boomer retirements, even though the adjustments due to the Greenspan Commission in the early 80s were supposed to pay for the boomers' retirements. This year the fund is running a (small) deficit, and so out of all the sources of the broader federal budget deficit (of which rising medical care costs, not to mention high defense budgets) it is social security that is the Big Problem that Something Must Be Done About (along with Medicare). I would agree that more immigrants will help in the short run, but demography is not the main problem here.
I and Bruce Webb have posted only about a million times in the past here and elsewhere on how if the "optimistic" projection of the SSA were to hold, the system would never run a deficit. In many recent years the economy beat that projection. However, in the last few it has plunged far below the pessimistic forecast with fica revenues collapsing as employment has collapsed in the Great Recession. This is the problem, and the simple solution is to get the economy and employment growing again at something like the optimistic forecast rate. Then the system will go back into surplus, possibly even mostly staying there, without any fiddling with or opening the doors to massive immigration (and, no, I am not anti-immigrant at all here, just trying to be clear about what is what).
Indeed, the fallaciousness of this general demographic hysteria is seen in that the US has among the best demographics for this even with low immigration compared with other OECD economies. Germany (and others) have the age distributions the US will have in 2030 when we hear Doom will hit, and they are paying their pensions all right, with Germany's even higher than the ones here. Really, folks, higher immigration may be an OK thing, but it is relatively peripheral to the condition of the Social Security system. Growing the economy and particularly employment is the key to saving the system.