By Patricia Zengerle and Richard Cowan
WASHINGTON (Reuters) - The U.S. Senate may not vote this week on the authorization for the use of military force in Syria, congressional aides said on Tuesday after Syria's recent acceptance of a Russian proposal to give up its chemical weapons.
Congressional leaders also want to wait to assess the American public's response to President Barack Obama's address on Syria on Tuesday night, several aides said.
Senate Democratic leader Harry Reid on Monday abruptly backed off plans to schedule a test vote on Wednesday on a White House-backed resolution to authorize military strikes on Syria, but aides said then a vote was still likely later in the week.
On Tuesday, a Senate Democratic leadership aide said it was unknown whether the Senate would cast any votes this week on the Syria resolution.
"We want to give the president a chance to make his case," the aide said.
Reid said on Monday he believed he had the votes in the Senate to pass an authorization for the use of military force.
Separately, Republican John McCain and other Democratic and Republican senators were working to modify the Senate resolution to include a "strict" timeline for Syria to turn over chemical weapons.
But both Democratic and Republican lawmakers have expressed doubts and enthusiastically backed the idea of allowing at least a short window of time for the world to react to Russia's plan to put Syria's chemical weapons under international control.
Mitch McConnell, the top Republican in the Senate, said on Tuesday he would vote against the current resolution authorizing U.S. military force in Syria, a blow to chances of passing the measure.
The three other top congressional leaders - Reid, House Speaker John Boehner, and House Democratic leader Nancy Pelosi - declared their support for military action last week.
TOUGH FIGHT IN THE HOUSE
In the House of Representatives, where Republicans control the majority of seats, the fight to approve the use of military force in Syria was expected to be much tougher than in the Senate, where Obama's fellow Democrats hold a slim majority.
House leaders had not yet even announced whether they would write their own authorization to use force, vote on the Senate measure or take some other approach.
"We are all working on the assumption that there will be no vote in either chamber in the near future, if at all," one senior Democratic House of Representatives aide said.
Boehner said on Tuesday the president must make a stronger case on Syria.
"The American people have not been supportive. They have not made the sale to the American people. That's why I think tonight is so important," he said at a news conference.
But Boehner also said it was important for Congress to help Obama present a united front. "I believe that it is important to try to help the president to provide a unified front in our effort to make it clear that the use of chemical weapons is clearly unacceptable," he said.
White House chief of staff Denis McDonough told Democratic members of the House on Tuesday that diplomacy, rather than military action, is the priority on Syria, U.S. Representative Gene Green told Reuters as he left the briefing.
Green, like many lawmakers, said he had been getting emails from constituents saying they wanted a diplomatic solution, and added, "That's what happening now."
Another Democratic lawmaker, Representative James Moran, noted the deep opposition among both Democrats and Republicans in the House to the resolution.
"I can't imagine we will have a House vote on this issue," Moran told reporters.
(Additional reporting by David Lawder and Thomas Ferraro; Editing by Doina Chiacu)