So what would happen if Villaraigosa left office early?*

Not to jump the gun, but in the event that the mayor is nominated to be Transportation Secretary (Ray LaHood resigned this morning), the City Council would almost certainly fill the vacancy by appointment. If that were to happen, Council President Herb Wesson would most likely be the man. (Theoretically, the council could also hold a special election, according to the City Charter, but that would be impractical given how close we are to the regular election.) Who knows whether any of this would affect the actual mayoral race, but it could provide a twist to the March vote to raise the sales tax, which is being pushed by Wesson. It also could impact this year's budget talks. As for the transportation job, Villaraigosa isn't the only candidate. From the NYT:

Several people have been mentioned as possible replacements for Mr. LaHood at the Transportation Department. Among them: Antonio Villaraigosa, the Democratic mayor of Los Angeles; Ed Rendell, the former governor of Pennsylvania; Debbie Hersman, the chairwoman of the National Transportation Safety Board; and Jennifer Granholm, the former Democratic governor of Michigan.

*Update: Raphael Sonenshein, executive director of the Edmund G. "Pat" Brown Institute of Public Affairs, helps clarify the appointment procedure. Basically, the Council President immediately takes over as acting mayor. But that doesn't preclude the council from making an appointment later on.

Sec. 243. President and President Pro Tempore. (a) The Council shall elect one of its members as presiding officer, who shall be called the President of the Council. In case of any vacancy in the office of Mayor pending appointment and qualification of a successor, or in case of unavailability due to sickness, absence from the state, or disability of the Mayor, the President of the Council shall act as Mayor of the City. The President of the Council, while acting as Mayor, shall not lose his or her rights as a member of the Council.