That’s a GOP aide talking about the Senate, not the House. He thinks the White House only gets it through the Senate now if it convinces enough moderate Democrats to vote to go to final passage, even though they oppose the resolution. Then, it can pass with 51.
If President Obama manages to squeak it by the Senate, he then may want to consider going to some fig-leaf, face-saving diplomatic maneuver, pocketing the support of one house of Congress and avoiding defeat in the other.