The biggest reason for a Switcheroo would be if the gender gap that has proved essential to Democrats in recent elections were suddenly to close, sending Obama (whose current approval rating is a paltry 40 percent) even further south in the polls. With white men already lost (Obama got only 41 percent of them in 2008; 9 percent in Alabama), a historic ticket with an African-American and a woman would have little downside.

The president’s more immediate political problem is with independents. We don’t know yet how much Clinton’s presence on the ticket might help with them (especially women) or with traditional Democrats. During the 2008 primaries, Clinton showed more strength than Obama among blue-collar voters in states like Pennsylvania, which is essential to the president’s re-election. (Although Biden, born in Scranton, is also popular there.)

In a larger sense, the move would lend excitement to what will inevitably be a sour and dispiriting campaign. Imagine the unemployment rate doesn’t budge and Obama goes into the Democratic National Convention in Charlotte, North Carolina, in early September trailing by six points with a mere eight weeks until Election Day. The Switcheroo may be his only shot.