While there have been posts about the TSA asking for a passport for international flights, they really don't have requirement to do so. They should accept any acceptable form of ID at the checkpoint.
I think you will have a much easier time because your other ID's include both names. Nor do I think your passport would be an issue at all now that you mention the maiden name is also on the ticket.
I would still get it changed as soon as the trip is over, and I would still bring the marriage certificate, but with both names on the ticket it should not be too much of a hassle. Leave some extra time just in case, but I think you will breeze though.