Hey, why not?  Hillary Clinton would be a shoe-in to win, and she’s going to be available to run very, very soon — although the exact timing might depend on whether Barack Obama appoints John Kerry or Susan Rice to replace her.  In fact, she’d probably get bipartisan support, since a four-year term as Bloomberg’s replacement would all but extinguish any chance of getting Hillary to run for President (via The Week):

Mayor Michael R. Bloomberg has long struggled to imagine a successor with the combination of star power, experience and grit to fill his shoes.

But not long ago, he was struck by an inspiration: Hillary Rodham Clinton, the retiring secretary of state.

In a phone call confirmed by three people, Mr. Bloomberg encouraged Mrs. Clinton to consider entering the 2013 mayor’s race, trading international diplomacy for municipal management on the grandest scale. She would, he suggested, be a perfect fit.

Much about the call, which occurred some months ago, remains shrouded in mystery. But Mr. Bloomberg’s overture to the former first lady highlights the level of his anxiety about the current crop of candidates, his eagerness to recruit a replacement who can rival his stature and his determination to become a kingmaker in the political arena he will soon exit.

In Mrs. Clinton, it seems, a mayor known for his sometimes unsparing critiques of those in public life sees a globe-trotting problem solver like himself.

Unfortunately, the New York Times reports that Secretary Clinton isn’t terribly interested in serving as Bloomberg’s protege.  Or, perhaps, she might want to buy a Big Gulp in the next four years, a possibility which Bloomberg has all but precluded in the Big Apple during his third term as mayor.

Mostly, though, a campaign for mayor would interfere with Hillary’s two potential career tracks after her resignation as Secretary of State becomes official.  Rather than run a city, she might decide she wants to succeed Obama, and so far polling shows that to be a real possibility.  Salon’s Steve Kornacki wrote last week that potential contenders for the Democratic nomination might even clear the field for her if she chose to run, although that prediction didn’t come to pass in 2008 when it seemed more likely.  Regardless of whether she ran as Hillary Clinton Private Citizen or Mayor Hillary Clinton of New York City, it’s almost certain that she’d have to run against Andrew Cuomo, who’s currently governor of the state.

The other career track?  Kingmaker.  Bloomberg wants to play kingmaker in New York City, but Hillary and Bill could do the same on a national scale, if Hillary chose to stick to retirement.  Even Barack Obama had to go to the Clintons for help in 2012 to get past Mitt Romney.  The two of them would wield enormous influence on the open 2016 primary if they chose that kind of role, and at 69 years of age by the time of the 2016 election, Hillary might prefer that to two years of hard campaigning.