When you do the math, as Galston has done, Obama will probably get no more than a fifth of the Republican Party in the House, which would be 47 votes (out of 233) and even that might be high, which means Democratic leader Nancy Pelosi would need to deliver 170 votes, or 85 percent of the Democratic caucus. She’s not there yet, but it’s not impossible. One crucial bloc of votes is the Black Caucus, which has 43 members, enough to sink the resolution or put it over the top.

“Once you get beyond the argument about the dead children and the U.S. role in the world, it comes down to saving the presidency itself and not allowing Barack Obama to fail,” says Paul Equale, a Washington lawyer and longtime Democratic activist. “That argument is best made to the Black Caucus, and that’s where you go for those votes.” National Security Adviser Susan Rice will be briefing the Black Caucus on Monday, one in a blizzard of briefings directed at influencing a vote for a resolution that many members might say privately they would like to see pass; they just don’t want to be the one casting the vote that could come back and haunt them in the next election.