I hooked a 3way for my second floor. I bought 20 amp switches, one for the top of the stairs and one for the bottom. I wired all of it correctly as I have checked and rechecked a lot of times. There is a 15 amp breaker where I'm pulling power from. When I tried the switches, the one at the bottom of the stairs does not turn off the light but when I hold the switch at halfway it works to turn it off? Is this a faulty switch or is it because my breaker is 15 amp and my switches are 20 amp?

The chance that the disparity of the amps is causing this issue is zero. You have maybe a 1 % chance the switch is broken leaving a 99% chance you have wired it wrong. http://www.youtube.com/watch?v=LDyvcM0gcVs

Holding the switch halfway means nothing and most likely prevents any connection whatsoever between the conductors hooked to the switch, so the circuit is broken and of course, the light goes out.
Post a diagram of how you wired the two 3 way switches and one of the experts here will likely determine what the problem is.