The U.S., Canada and Mexico are focusing on rewriting the auto rules at the center of the North American Free Trade Agreement as negotiators face hard deadlines in an election year, raising the possibility of less drastic changes to other controversial parts of Nafta, according to people following the talks.

A Republican congressional aide spoke of a possibility of negotiators striking a “skinny deal” on Nafta that would include a thorough rewrite of the complicated rules that govern which cars and auto parts can be traded...