By Jeff Zeleny and Arlette Saenz

With skepticism on Syria rising in Congress, President Obama delivered a personal pitch on Capitol Hill, meeting behind closed doors in rare back-to-back sessions with Senate Democrats and Republicans.

The message from the White House: Withhold opposition to Syria plan until a potential diplomatic lifeline runs its course.

A bipartisan coalition of senators, led by Sen. John McCain and Sen. Chuck Schumer, are working to craft an alternative to the Syria use-of-force resolution that has been losing momentum and support in Congress.

The alternative resolution aims to give the United Nations time to take control of Syria's chemical weapons, aides told ABC News, and would require the removal of chemical weapons in Syria by a specific date. If that failed, the resolution would authorize military force.

Senate Minority Leader Mitch McConnell, who had remained skeptical but undecided, voiced his opposition to the original Syria proposal. It was a rare departure from a top Congressional leader with a president's request for military action.

"A vital national security risk is clearly not at play, there are just too many unanswered questions about our long-term strategy in Syria," McConnell, R-Ky., said on the Senate floor.

Speaker John Boehner took a different view, saying that he still supports the administration's call for limited military strikes on Syria. A majority of the House opposes the plan, but Boehner said he had never defied a president's call for using force and would not do so now, despite saying "a lot of mistakes" have been made by the administration on Syria.

"There's one person who speaks for the United States of America when it comes to foreign policy, and that's the president of the United States," Boehner said. "So I think it's critically important that when the president goes out on behalf of the American people, that the members of Congress do everything they can to be supportive of him. "

The first vote on Syria was expected to take place Wednesday in the Senate, but Majority Leader Harry Reid called for a delay. He said diplomatic avenues needed to be pursued, but said today on the Senate floor that the Syrian government needed to prove its willingness to cooperate with the United Nations.

"The Assad regime must act quickly to prove their offer is real," Reid said, "not merely a plot to delay military action or action of the United States Senate."

As the administration continued its intense outreach effort to lawmakers, holding a series of briefings at the Capitol and in the White House, Democratic leaders conceded that passage in either the House or Senate seemed increasingly unlikely. But they said the situation was fluid and momentum could grow for a diplomatic solution.

"Let us pray the Russian proposal is one that will avoid the use of force," Rep. Nancy Pelosi, the minority leader, told reporters at a news conference.