While President Barack Obama spent the morning behind closed doors rallying the bipartisan congressional leadership to his side, an equally important hurdle for his Syria policy comes this afternoon, when 18 senators on the Foreign Relations Committee will publicly reveal whether they’re for, against or undecided on authorizing U.S. military intervention.

The White House’s basic strategy for getting congressional approval of the president’s plan of attack looks to be simple: Lobby hard to secure a strong bipartisan majority in the generally more interventionist Senate during the first half of next week, and hope that show of support assist the president in persuading a narrow majority in the more skeptical and isolationist House to go along.

How easily that approach can be sustained will become clear soon after the committee convenes Tuesday at 2:30 p.m., but the initial indications look promising for the president.

Obama has already won over at least three of the four Democrats on the panel who voted “no” the last time Congress was asked to authorize military action – when it gave its blessing to the Iraq War 11 years ago this fall.

They are committee Chairman Robert Menendez, who was a New Jersey House member back then; Richard J. Durbin, the majority whip and Obama’s former Illinois colleague who led opposition against the Iraq authorization and the measure permitting the Persian Gulf War back in 1991; and Barbara Boxer of California. Benjamin L. Cardin of Maryland, who was also in the House for the last war vote, is the Democrat who’s said he’s waiting until the administration has made its best case before deciding.

Only two Republicans on the committee were in Congress for the Iraq War vote: John McCain, Obama’s most influentially hawkish critic, who on Sunday said he could support the sort of limited strike the president’s calling for, and his fellow Arizona senator Jeff Flake, a supporter of the Iraq campaign as a House member in 2002 who is publicly uncommitted on Syria this time.

More attention will be paid at the hearing to the two Republicans who are moving toward presidential campaigns in 2016, and who could see their aspirations fueled or stalled by the votes they are about to cast on Syria. Marco Rubio of Florida has said he’s undecided but has sounded open to being persuaded. Rand Paul of Kentucky is expected to lead the chorus of tea party/isolationist Republicans who will argue that intervening in Syria is not in the United State’s national security or economic interests.

The only other Republican senator on the committee who’s sure to take Paul’s side is Ron Johnson of Wisconsin. Jim Risch of Idaho and John Barrasso of Wyoming have not revealed their positions and are preparing skeptical questions for the witnesses, while ranking member Bob Corker of Tennessee is an all-but-certain “yes” vote.

Among the other Democrats, Bob Casey of Pennsylvania and Chris Coons of Delaware have publicly declared themselves ready to vote for the authorization resolution, and Tim Kaine of Virginia has come very close to unequivocal support. Tom Udall of New Mexico and Jeanne Shaheen of New Hampshire say they’re  undecided, while Christopher S. Murphy of Connecticut is the only member of the president’s party on the committee who has come out publicly against taking any military action in Syria.