One of the central, driving questions in our politics is this: Why are people who are themselves reliant on government programs so prone to electing anti-government politicans who want to put them on the chopping block?
When we ask this question, I think you really have to distinguish between Social Security, Medicare, and everything else. Like it or not, most people simply don't think of Social Security and Medicare as "safety net" programs. They think of them as programs they've paid into all their lives and are now simply drawing down from. It's basically their own money being returned to them, not a "government program."
But there's another piece to this question that I think gets less discussion than it deserves: a lot of voters don't take seriously Republican bluster about cutting safety net programs, and they don't really trust Democrats to save them either. So from an electoral perspective, the contrast between the two parties isn't as great as it seems. The bottom line is that a lot of voters like the idea of talking tough about the safety net — it shows that your heart is in the right place, especially if you're talking about parts of the net for other people — but they don't really want the net slashed in real life. Republicans mostly deliver that combination. What's more, even if they get a little carried away, Democrats will stop them for purely partisan reasons. What's to get worked up about?
That may change if the tea-party wing of the GOP really takes over and a Republican president gets elected, but even then I suspect it won't change a lot. In fact, the recent deal over the payroll tax cut/doc fix/unemployment benefits bill suggests that even tea-party-ized Republicans can get chastened pretty quickly after a few weeks back home during an election year. They'll keep up the bluster, but they're not going to make any big cuts to the programs that their constituents truly want to keep. I think most of the people who vote for them understand this pretty well.