Although Mr. Obama has asserted that he has the authority to order the strike on Syria even if Congress says no, White House aides consider that almost unthinkable. As a practical matter, it would leave him more isolated than ever and seemingly in defiance of the public’s will at home. As a political matter, it would almost surely set off an effort in the House to impeach him, which even if it went nowhere could be distracting and draining.

As a result, Mr. Obama would be even more reluctant to order action in the one case that has most preoccupied military planners: the development of a nuclear bomb by Iran. Any operation to take out Iranian nuclear facilities would require a far more extensive commitment of military force than the missile strike envisioned against Syria. Moreover, a rejection of the Syria strike would make Mr. Obama less likely to leave behind a robust force in Afghanistan after combat troops are withdrawn at the end of 2014.

“I think this vote determines the future of his foreign policy regardless of whether it’s a yes vote or a no vote,” said Rosa Brooks, a former top Defense Department official under Mr. Obama. “If he ekes out a yes vote, he’s beholden to the Republicans.” But, she added, “if he gets a no vote and stands down on Syria, he’s permanently weakened and will indeed probably be more inward looking.”