Can a thief steal at level 1 given that failing to steal causes the thief to lose a level?
The Official Munchkin FAQ says Yes.
Q. What happens to a Level 1 Thief who fails an attempt to steal? Does he die?
A. Nothing happens to him. You can't go below Level 1. (Beware the Level 1 Thief – he literally has nothing to lose!)
We have played it this way. I've not found anything in the rules that indicates that you need to be able to cover the cost of failing before attempting the theft. Also, this is probably the best time to use the Theft ability since your level can never go below 1.