I had a similar experience trying to book with AM. Apparently their "systems" are rejecting several credit cards that aren't MasterCard. Since I don't have a MC, the best suggestion they could come up with was that I either use Western Union (no way) or that I drive to the airport and pay at the counter. Long story short I decided to let my reservation expire. Pretty awful from a customer service standpoint.
Separately - does anyone have suggestions on how to make this deal work from IAH? I've seen it available from many cities, but no Houston unfortunately...