If you want to replay 2004 and assign roles, I see Thompson as Dean, not Rudy, Thompson is the newcomer.
Dean started running as early as anyone in 2003. He was a newcomer only in the sense that he had not been well known before his presidential campaign propelled him to prominence because a fragment of his party passionately supported him. His campaign fell apart because, in spite of all the hype, it became clear that he couldn’t unify that party for the general election. Democrats wanted to win so they turned away from the guy that their left wing loved and nominated somebody who could hold their coalition together and compete with George W. Bush. This happened in the runup to Iowa. By the time Dean issued his famous scream his candidacy was already over.
Rudy’s situation is exactly parallel. He is beloved of the leftmost wing of the Republican Party which lets him reach the high 20’s in early polling. But he can’t unify the GOP any more than I can fly without mechanical assistance. Just as Democrats turned away from the divisive Dean, Republicans will turn away from the divisive Giuliani.
Remember, you heard it here first.