Well, they probably wouldn't. They might have a slightly more generous SSI program, which would be income and asset tested. Same for public education...
The point is we've moved away from "there are just certain things government does well and should do" and over to "maybe government should do some stuff for the poor but that's about it." It's a problem, both from a policy perspective, as there are certain things the government should do, and from a political perspective, as benefits-for-other-people never gets wide support.
Imagine what the centrists would say if universal government-run mail delivery was proposed today.