2003 Pontiac Grand Am problems starting--Distributer? Elect

I have a 2003 Pontiac Grand Am. It has been having trouble starting, but once it starts its fine. I actually had to have it towed to a mechanic because it wouldn't start. Once there (of course) it started right up, and the guy told me that unless you catch the car doing whatever the problem is--its hard to diagnose it. The car will go days and be fine--then jsut all of sudden not start--it sounds like it will, but it wont turn over. Sometimes if I give the car a little pish, it starts up? What could be the problem? It almost sounds like something isn't catching?