He's stuck. He wouldn't say what the offer was or who specifically made it.
He can't simply said "I lied about it!" but he's not going to willingly supply any new information.
He may have a good hand, but it's not a card game he wants to be in anymore. He doesn't want to play against the Democrats now that he's one of them.
Maybe, but then he could have just come out and said “I misinterpreted what I thought was an offer but which really wasn’t.”
Instead, he doubled down.