I actually think that if the government collapses, the FDIC is the absolute last thing to fail. Every politician understands how much of a political suicide it would be to directly fail the voters so they lose something they own in a very personal way. (As opposed to the typical government malfeasance, where the losses come from large, impersonal pools.)

If government were to collapse, I expect the last thing that the politicians would be concerned with would be the FDIC. First thing in their minds would be how to spin this so they don't end up on the business end of a militia firing squad.