would running out of gas burn up a jeeps fuel pump?

Yes, that is the most likely problem. Between the age of the vehicle and running it dry, the pump is probably toast. You can sometimes get an in-tank pump to run for a short time by locating the pump (usually a well in the tank formed by a small dip), and hitting the bottom of the tank in that area with a rubber or wooden mallet. If the car starts, keep it running until you get where you're going, because that trick only works once.

yeh running outa fuel will toast a pump on the early jeeps especially, later models have a no fuel shut-off, but not the 90's...replace it and replace the hose and filter at the same time-saves problems later...good luck

You betcha.

The fuel pump is in the fuel tank, and fuel around the pump is what keeps it cool. Run it dry, and that little motor has been running without cooling for a while - inside a closed fuel tank, so it can't even get air rushing past to cool it off.

Fortunately for you, fuel pumps aren't too expensive nor difficult to replace. You will have to drop the tank, though.

But hey, it's already empty - what better time than now?