A steady stream of rank and file House Republicans have announced their opposition to a resolution, with House Speaker John Boehner expressing support for a strike but making it clear it's up to the White House to secure the votes.
The pressure is on for Democratic leaders to convince a significant chunk of war weary House Democrats to back the president.
Even within top Democratic leadership ranks there are divisions.
Democratic Leader Nancy Pelosi and Democratic Whip Steny Hoyer support the president, and are in close contact with the White House.
But the No. 3 leader, Rep. Jim Clyburn is not aboard yet.
"Issues of war & peace require thoughtful consideration. I reserve judgment on Syria until a resolution and more details are forthcoming," Clyburn said in a statement released via Twitter.
House Democratic Caucus Chairman Xavier Becerra, however, is now saying he is prepared to vote 'yes' if the military response is limited.
While Pelosi and Hoyer aren't formally putting pressure on members, they are soliciting input on the language members could support for a resolution.
For the second time in two days, Pelosi sent a letter to House Democrats urging them to attend classified briefings and review the report laying out the evidence on the use of chemical weapons.
"I don't know. I think it would be important to get a majority in the Congress. But I don't know if it's important how you would break it down. These issues are not really partisan," she said.
Cleaver was reluctant to characterize the breadth of opposition among his colleagues.
"There is a great amount of skepticism floating over the Capitol," he said.
More classified briefings
Cleaver added that the support among party leaders in Congress for a military response is unlikely to sway fellow House Democrats.
Two more classified briefings with administration officials are scheduled for Thursday and Friday. But most members are still out of town for the congressional recess and will not have a chance to review the evidence until another closed session set for Monday evening, the first day Congress is officially back at work.
But the issue has many Democrats mindful of what's at stake if they oppose their president.
Cleaver said he was "invested in the success of President Barack Obama" and wanted history to judge his presidency "more positively than negatively."
Schakowsky also referenced history as she wrestles with her vote.
"As a Jew, I am mindful how the world stood by when millions of Jewish people were gassed to death and feel an obligation to oppose such actions," she said. "The question remains what's the most effective way to make clear to the world that the U.S. will stand against such atrocities."