The American Civil Liberties Union came out publicly to explain their Larry Craig support:

The [ACLU] supports Senator Larry Craig’s attempt to have his guilty plea withdrawn because the Minnesota law under which he was arrested is unconstitutionally broad. The statute punishes “offensive, obscene or abusive language” which tends to arouse “alarm, anger or resentment” in others. Clearly, this law has the potential to ensnare and criminalize legal, constitutionally protected free speech, including solicitation for private sex.

The Minnesota Supreme Court and other courts have found that a closed bathroom stall is a private location. The police have no business spying on people in places where there is an expectation of privacy. The ACLU is in no way advocating sex in public bathrooms. If law enforcement is genuinely interested in stopping sex in public bathrooms rather than ensnaring people in sting operations, posting a sign prohibiting it and announcing police patrols would be much more effective and would meet constitutional requirements.

Also, Craig's political action committee, Alliance for the West, has closed up shop.