Recent opinion surveys show intense American skepticism about military intervention in Syria, even among those who believe Syria's government used chemical weapons on its people.
Congress, perhaps, is even more dubious.
"It's an uphill slog," said Rep. Mike Rogers, the Republican chairman of the House Intelligence Committee who supports strikes on Assad.
"I think it's very clear he's lost support in the last week," Rogers added, speaking of the president.
Complicating the effort in the Senate is the possibility that 60 votes may be required to authorize a strike.
Republican Sen. Rand Paul of Kentucky said he would consider a filibuster, but noted the delay tactic was unlikely to permanently nix a vote. Paul would, however, insist his colleagues consider an amendment to the resolution that would bar Obama from launching strikes if Congress votes against the measure.
Still, Sen. Harry Reid, the Democratic leader, has predicted authorization and McDonough, too, on Sunday telegraphed optimism.
"They do not dispute the intelligence when we speak with them," McDonough said, of members of Congress.
But while the public discussion lacks a direct link between Assad and weapons, the private briefs are no better, two lawmakers said.
"The evidence is not as strong as the public statements that the president and the administration have been making," said Rep. Justin Amash, R-Mich. "There are some things that are being embellished in the public statements. ... The briefings have actually made me more skeptical about the situation."
Rep. Buck McKeon, R-Calif., said "they have evidence showing the regime has probably the responsibility for the attacks."
But that's not enough to start military strikes. "They haven't linked it directly to Assad, in my estimation," said McKeon, chairman of the House Armed Services Committee.
McDonough, an Obama foreign policy adviser dating back to his 2008 presidential campaign, said the dots connect themselves.