Craig may not resign?

So says MSNBC:

BOISE, Idaho - Sen. Larry Craig is reconsidering his decision to resign after his arrest in a Minnesota airport sex sting and may still fight for his Senate seat, his spokesman said Tuesday evening.

Apparently this is Arlen Specter's fault:

A telephone call Craig received last week from Sen. Arlen Specter, R-Pa., urging him to consider fighting for his seat is affecting Craig’s decision to reconsider his resignation, Smith said.

Quit, don't quit, whatever.

My only question is one of process. Craig was traveling home during a session of Congress when he was arrested and detained and questioned for the act that he eventually pled guilty to as a misdemeanor.

But according to the U.S. Constitution:

They shall in all cases, except treason, felony and breach of the peace, be privileged from arrest during their attendance at the session of their respective Houses, and in going to and returning from the same;

What he did certainly wasn't treason, and he pled guilty to a misdemeanor, not a felony. Was it a "breach of the peace"? Well, he didn't do anything to anybody, or hurt anybody, or cause a stir or a ruckus or in any way disrupt the ordinary lives of others.

But it is also true that the "crime" for which he was originally detained was a felony -- although how "signalling" that you'd like to have sex with someone is a felony is something I don't understand. I'd understand actually HAVING sex in the bathroom might be a serious offense, but simply attempting to pick someone up in the bathroom, someone who by testimony was ENCOURAGING your advances?

What if Craig wanted to take the guy to a hotel room, or the back seat of his limo? Neither of those acts would be a crime, and if so, would arranging the hookup in a bathroom be a crime?

Anyway, I probably wouldn't vote for a guy that was trying to pick up strangers in a bathroom, either male OR female. Which is good enough reason to resign. But I wonder why nobody's discussed the constitutional ramifications of this case?

I know that stories are around of Senator Byrd getting out of traffic "jambs" at least once by use of his pocket constitution.