Volkswagen Beetles are adorable, especially when people put eyelashes on them. But just because something is cute, doesn't mean it's reliable. Just look at the mogwai.
Billy's VW Beetle doesn't work. We hear Mr. Futterman blame the car's failure to start on its German origins:
MR. FUTTERMAN: These goddamn foreign cars always freeze up on you.
Mr. Futterman feels that way because of WWII fears of gremlins, which were believed to have been planted on British and U.S. planes by Germans to make them crash. (Source) Therefore, he's suspicious of the German car, no matter how cute it is.
Ironically, the car miraculously starts when Billy needs it, and he uses it to rescue Kate from the bar. Then it dies again, which forces them both on foot for the remainder of the movie. Maybe there was a gremlin in it?
The real question we have is about the pink car Gizmo drives at the end. Is it American made? Someone check under the hood.