So, what do we learn from this Senator Larry Craig thing?
Once you plead guilty, it is much harder to say, "I didn't do it." The way the average American looks at this now is, "If you didn't do it, you wouldn't have pleaded guilty. You would've wanted to scream the injustice from the rooftops 'I didn't do it! I've been framed!'" But, instead, once you plead guilty, you're kind of stuck with it.
(Similarly, if you didn't do anything wrong, why would you resign? Why not fight it out and try to prove your innocence? Why bother to apologize but then follow it up with "I cannot control what people choose to believe?" )
This happens all the time in criminal courts. Someone's criminal record is questioned, and they respond, "I didn't do it, I just pleaded guilty to..." either avoid a hassle, or save money, or for any other reason. But this just doesn't fly, because the next logical question is, "Ok, then you lied to a judge, under oath, when you said you did it?"
But from a criminal defense perspective, the point is, it is very hard to overcome a guilty plea, or to overcome a criminal record.
Think long and hard before pleading guilty (especially to things you are not guilty of), it could be something that scars your record (and people's opinion of you) for a long time.