Never really a good sign. It sounds like you are in no position for making a commitment and the only way out of the situation is to take yourself out. Stop waiting for the girlfriend to break up with you. If she didn't after you cheated on her, she's probably trying to trap you.
It's awful, I know. But some women care so much about getting married that they don't care if it's too the right person or not.
Trust your gut. If it says walk away, walk away.