SS is a way for the recipients (old people) to tax workers, therefore the more people getting SS the stronger the program is.
That seems obvious, but let me apply a little public choice reasoning to argue that it goes the other way: the more people getting Social Security, the weaker will be the support for the program. Rather than start from scratch, I'll just quote from a piece I wrote on this in Policy Review, April/May 2006. The article is titled "Why Spending Has Got to Give."
Consider, for example, one way the political dynamics of Social Security might change as more and more baby boomers (those born between 1946 and 1964) start collecting benefits. One of the most important insights from "public choice" economics is what I like to call "the importance of being unimportant." Translation: If an interest group is suitably small, its members can be relatively cohesive. They can get together to obtain a special subsidy, regulation, or import barrier that costs members of a much larger group a little each in order to give members of the small group a lot each. One reason the farm lobby has been so successful at getting subsidies for its members is that there are so few farmers. This means that each farmer can get a substantial gain at the expense of consumers and taxpayers (in the form of higher prices and higher taxes, respectively) and that the consumers and taxpayers don't bother organizing to fight the wasteful farm policies because each pays a much smaller amount than the gain per farmer. This "importance of being unimportant" explains a phenomenon that has surprised many observers: Even as the farm population has shrunk, the lobbying success of the farm lobby has grown.
But the reverse also holds. All other things being equal, the larger the interest group becomes relative to the size of those paying for its special privileges, the bigger becomes the loss to the payers. The case of Social Security and Medicare now becomes relevant. One reason there has been relatively little resistance by the working population to increased subsidies to the elderly is that for a few decades there have been about three to four workers for every elderly beneficiary. But as the number of workers per beneficiary falls to 2.2 by 2030, as noted above, the resistance among workers will grow because the cost per worker will grow. This could imply a new political equilibrium in which the amount of benefit per elderly person would not grow as quickly as planned and might even fall somewhat. Readers of Malcolm Gladwell's The Tipping Point might think that that is what I'm describing here. But it's not necessarily a tipping point. Rather, increased political pressure by the relatively young will lead, along a continuum, to a different outcome.
Now, the above does not mean that there would be an across-the-board reduction in benefits or in the growth of benefits for all the elderly. Instead, a new political coalition might form between the working-age population and, say, the oldest Social Security beneficiaries to rein in benefits for the relatively young seniors who can most afford to give some up. Or it may be a coalition between the working-age population and the younger elderly. Which coalition comes about is difficult to predict -- that there will be a coalition seems likely.