Car wont start in the Morning after sitting all night

My car has a problem that no one seems to be able to diagnose. In the morning (or first time I drive it that day) I turn the key on and nothing happens. Radio comes on etc, but no fire. If I try a few times, then go away for a few minutes and come back, it starts up fine. Subsequent starts may be delayed a second or two, or may just start right up. If I jiggle the key, it starts right up. The problem is getting worse. My mechanic thinks its the starter, but it does not seem like that is it, since subsequent starts are okay, and this only happens on the first start of the day (usually). I have to leave it alone after the initial tries for about five minutes. I turn on the key and either hold it in the on position or jiggle the key to get it to turn over. Can you give me some idea of what to do? Thanks