Congress’s approval of a military strike against Syria was in doubt Tuesday despite calls of support from congressional leaders in both parties.

Speaker John Boehner (R-Ohio) and House Majority Leader Eric Cantor (R-Va.) said they would vote in favor of military authorization, but a running Whip List created by The Hill showed their conference was leaning against the measure.

More than 30 House Republicans were publicly saying they would vote against a military strike as of Tuesday evening, compared to only four who said they would back it.

Boehner’s office also said he would not whip support for the measure and that winning the vote would be President Obama’s responsibility. 

“Everyone understands that it is an uphill battle to pass a resolution, and the Speaker expects the White House to provide answers to members’ questions and take the lead on any whipping effort,” Boehner spokesman Michael Steel said in a statement.

“All votes authorizing the use of military force are conscience votes for members, and passage will require direct, continuous engagement from the White House,” Steel said.

Given the antagonism between President Obama and House Republicans, it will be difficult for Obama to win rank-and-file members to his side.

This could put more importance on a strong Democratic vote, though war-weary House members in that party are no sure pool of support.

Minority Leader Nancy Pelosi (D-Calif.) on Tuesday aggressively lobbied her conference to back the president’s call for action with public comments and a letter, though her office said it was not formally whipping on the issue.

Prospects for the president’s request looked much better in the Senate, where key lawmakers such as Senate Intelligence Committee Chairwoman Dianne Feinstein (D-Calif.) and Senate Foreign Relations Committee ranking member Bob Corker (R-Tenn.) offered support.

The American Israel Public Affairs Committee (AIPAC) also announced its support on Tuesday for military action, something that could swing votes in both chambers.

Secretary of Defense Chuck Hagel and Secretary of State John Kerry pressed senators to back the president during a Tuesday hearing in the Senate, with Kerry promising that no U.S. soldiers would set foot on Syrian soil.

Yet there were holdouts in the upper chamber, too.

Senate Republican Leader Mitch McConnell (Ky.) and Whip John Cornyn (Texas), who could each face difficult primary races next year, withheld support in a sharp contrast with their House counterparts. 

“While we are learning more about his plans, Congress and our constituents would all benefit from knowing more about what it is he thinks needs to be done — and can be accomplished — in Syria and the region,” McConnell said in a statement after meeting with Obama at the White House.

Sen. Rand Paul (R-Ky.), an important McConnell ally who has helped prevent conservative activists from uniting against McConnell back home, staunchly opposes an attack on Syria.

Cornyn is also wary of seeing a Tea Party challenger after Sen. Ted Cruz (R-Texas) defeated Lt. Gov. David Dewhurst in an upset in last year’s Republican primary in the state.

“It’s important that he bring Congress in but he needs to make the case to the American people and that case hasn’t been made yet,” Cornyn told reporters on Tuesday.

Democratic and Republican senators predicted privately the authorization of force resolution would pass the upper chamber by a large margin.

A Republican senator predicted it would also pass the House by a narrower vote.

Boehner’s and Cantor’s support is by no means a guarantee of success, however.

The Republican Conference has repeatedly bucked its leadership, most recently on the farm bill. A leadership-backed measure to prevent the “fiscal cliff” of tax hikes and spending cuts in 2012 never made it to the floor because of opposition within the conference.

Rep. Steve Israel (N.Y.), chairman of the Democratic Congressional Campaign Committee, said House Democrats are prepared to provide the bulk of votes for the resolution in the House.

In the Senate, while many lawmakers voiced skepticism about the effectiveness of a limited military strike, there is broad reluctance to countermand the nation’s commander in chief on an issue of national security.

“We don’t want to set a precedent that would tie a future president’s hands when he or she wants to use military force to defend national security interests,” said a Republican senator who is publicly undecided about supporting the force resolution.

Senate Foreign Relations Committee Chairman Bob Menendez (D-N.J.) and Corker, the top Republican on the panel, are negotiating a use-of-force resolution that was expected to be unveiled as early as Tuesday night. Corker predicted the panel would hold a markup on the measure in the next few days to prepare it for a floor debate and vote next week.

“I have a strong sense that we will be able to come to terms fairly quickly with what an authorization ought to say,” Corker said of his talks with Senate Democratic leaders over the resolution.

Lawmakers on the Foreign Relations panel said the measure would impose stricter limits on the president than the language already proposed by the White House. 

“The resolution presented by the president was too broad. We need to narrow that resolution,” said Sen. Ben Cardin (D-Md.), a member of the committee, who predicted a revised resolution would pass. 

Specifically, the Senate language would restrict the president from using ground forces against the Syrian government and limit the window in which he could use force, according to Senate aides. 

Sen. John McCain (R-Ariz.), however, warned his support could fall off if the authorization is too limited.

— Justin Sink contributed to this report.