Since it's Delta's fault they should put you on a equal flight even if they have to move you to one of their partners. I know that they are partners with American.
I just had a similar thing happen to me today with Alaska Air for my flights to Orlando in September. I called them and they moved me to better flights than what I had, the flights I am on now would have cost $$$ more.
Delta is NOT a partner of American. And generally they won't put you on another airline in this case.
Also, to the poster who is upset DL left a message at thier home, that's the number DL had. I always use my cell phone number when booking travel (now you see why) I don't even give them another number. ALL airlines are only going to make ONE call, the primary number.
(To all of you avoiding DL, NW, AirTran etc. what did you PAY??? We are getting what we are PAYING for and we are NOT paying enough for service! I read threads on here every day going "$200 round trip is TOO much" Well.... )

