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President Obama emerged from the G-20 summit in Russia acknowledging steep challenges in his attempt to garner support for a military strike against Syria from world leaders and members of Congress ahead of a critical vote on a use-of-force resolution.

Obama's international coalition appeared anything but strong as he prepared the nation from the White House Tuesday night on his push bid for public and congressional authority in response to a chemical attack on civilians last month that the U.S. says was carried out by Syrian President Bashar Assad's military.

"I knew this was going to be a heavy lift," Obama conceded Friday, adding that given the last decade of war, any hint of "further military entanglements in the Middle East" is viewed with suspicion.

The president spoke to reporters at the end of a two-day international summit, where he sought backing for a strike against Syria in retaliation for a deadly chemical weapons attack against civilians. But Obama appeared to leave the summit with no more backing than he had when he arrived.

In advance of the president's address, the administration will continue to lobby lawmakers hard. Fox News confirms that Vice President Biden plans to have dinner on Sunday night with Republican senators the administration thinks could be swayed on Syria -- ahead of a vote as early as next week.

Administration officials scheduled new classified briefings for lawmakers and White House chief of staff Denis McDonough will be making the rounds on all five Sunday talk shows. National Security Adviser Susan Rice on Monday will discuss Syria in a speech at the New America Foundation.

The president admitted Friday his campaign may not succeed.

"It's conceivable at the end of the day I don't persuade a majority of the American people that it's the right thing to do," he said. "And then each member of Congress is going to have to decide."

Though Obama won early support from House Speaker John Boehner and other congressional leaders before leaving for the G-20 summit, he's still facing resistance to a strike from rank-and-file members of his own party, as well as Republicans.

Boehner spokesman Brendan Buck gave a cautious assessment of the coming national address.

"The speaker has consistently said the president has an obligation to make his case for intervention directly to the American people," he said. "Members of Congress represent the views of their constituents, and only a president can convince the public that military action is required. We only hope this isn't coming too late to make the difference."

The president used his weekly address Saturday to reassure skeptical lawmakers that any U.S. military action against the Syrian regime would be limited and not an open-ended intervention.

"This would not be another Iraq or Afghanistan," Obama said. "There would be no American boots on the ground.  Any action we take would be limited, both in time and scope - designed to deter the Syrian government from gassing its own people again and degrade its ability to do so."

For now, U.S. lawmakers say their constituents are overwhelmingly against military action in Syria – a fact they weigh heavily as they consider how to vote.

Rep. Peter King, R-N.Y., one of the biggest advocates for military action on the Hill, acknowledged in an interview with Fox News that he’s not at all certain there are 218 votes in the House for the resolution to pass. Informal tallies show only a few dozen members of the House have come out for military action.

"It is up to the president to be much more forceful and not seem like he is trying to pass the buck on to someone else," King said.

House Democratic Leader Nancy Pelosi also said in an interview with Time that she’s not sure she can get a majority of her caucus on board.

Opposition to, and support for, a military strike cuts across party lines. Reluctant House members may be waiting to see what the Senate does before making up their minds. But even this week’s successful committee vote, which sent the resolution to the full Senate, exposed deep divisions – the measure passed on a narrow 10-7 split.

The president was also running into continued international resistance from some corners, and especially from Vladimir Putin, during his brief visit to St. Petersburg, Russia, for the G-20 summit. Still, at the close of the summit, 11 nations including the U.S. released a statement condemning the use of chemical weapons and calling for a "strong international response."

The countries signing the statement with the U.S. were Australia, Canada, France, Italy, Japan, South Korea, Saudi Arabia, Spain, Turkey and the United Kingdom.

Obama said he spoke with Putin, and had a "candid and constructive conversation," on the "margins" of the summit. But having already abandoned seeking support through the U.N. Security Council, Obama is focusing more on U.S. lawmakers and voters.

Putin said that the U.S. push for military action has been supported only by Turkey, Canada, Saudi Arabia and France. Putin said that German Chancellor Angela Merkel has taken a "very cautious attitude."

He said that many others along with Russia and China voiced their opposition to the military action, including India, Indonesia, Argentina, Brazil, South Africa and Italy.

"The use of force against a sovereign nation is only possible as self-defense — and Syria hasn't attacked the United States — and on approval of the U.N. Security Council," Putin said. "Those who do otherwise place themselves outside the law."

Meanwhile, the Kremlin said Russia was boosting its naval presence in the Mediterranean Sea, moving in warships into the area and stoking fears about a larger international conflict if the United States orders airstrikes.

Illustrating the risks associated with a strike, the State Department ordered nonessential U.S. diplomats to leave Lebanon, a step under consideration since last week when Obama said he was contemplating military action against the Syrian government.

The Associated Press contributed to this report.