The scene is perhaps misleading: The sound Emmit's car makes sounds a lot like a low fuel warning. But Emmit reacts by moaning "What now?" which is an odd reaction to running out of gas. It's true that Emmit was in an emotional state, and could have missed that he was low on gas to start with, but other car problems could cause the car to start beeping and stop working.
The scene actually played out a bit like a problem I had with my car's cooling system last winter. Leaving the engine off for a while was enough to let it cool down so I could get back to driving—luckily, that was the extent to which my experience mirrored Emmit's.
If we hypothesize that the alarm and malfunction was due to an overheated engine, there's no logical problem to worry about.