I'm going to confess that they only reason I'm writing this is because a good metaphor ran through my head while staring off into space because of the dullness of the book I'm reading on consumption tax policy and the taxation of capital income (a real thriller).
Anyway, much of the debate about interest groups seems to either take it for granted that interest groups are preexisting or that interest groups are created by government policies, and often always created whenever the government spends money. Neither of these perspectives are really anywhere close to accurate. Some interest groups exist based on other sources of power, others come into existence because of rumored changes in government policy, some become coordinated in response to external events, and some do come into being mostly as a result of government spending. There's nothing uniform about this.
Regarding just the government spending bit however, contrast Social Security with other anti-poverty programs, particularly Temporary Assistance for Needy Families (TANF or welfare). Social Security is just about politically inviolate, while some politicians will attack it reforms are generally minor and along the lines of what those designing the program intended (SS always required economic growth to pay for it, it was meant to maintain someone's relative income after all rather than be a pension scheme, they also knew that over 60 life expectancy was increasing, however they had poor data on it and it would have been impossible to design a workable formula with that data, still is really, so it was expected that tweaks would be made as necessitated to keep it functioning, reforms to things like retirement age is the program working as designed). In response to SS, a number of previously weak organizations combined or became organized becoming a very powerful lobby. There are a lot of reasons behind this, including program design, an easily identifiable minority it pertains to, once in the minority people stay there, and the fact that this minority is one that the majority eventually fall into. Thus, one of the most powerful lobbies on capital hill was born.
TANF looks a lot different. Its funding is smaller, but there has never been a comparable consolidation of interests to make for a coherent lobby. The weakness is overdetermined, there are a lot of differences among the groups it covers, funding streams are highly fractured, most people are only in the relevant minority for a short period of time, etc.
The differences in treatment are stark however. While SS is nearly untouchable, TANF is basically a pinata that gets beat with a rhetorical bat until the money comes out whenever a politician thinks they need money. And usually, more people join in with only a few lonely academics calling for the beating to be stop. This difference illustrates how government spending on its own does little to form interest groups, the characteristics of the potential group makes a big difference.