Clark's "Would Have Been A Republican If Rove Had Called" Joke

He stated this in jest and yet was still upset that he hadn't been called to help pull together a coalition. People use humor to offset their genuine anger all the time. This aside is being thrown out by Republicans who see that his voting past (before Clinton/Gore) is getting some play in public forums.

Can no one see that the joke doesn't make any sense unless he identified as a Democrat at the time?