President Obama announced Friday that he'll make his case to the American people next week for military action in Syria.

But with lawmakers lining up against the plan, some warn that a national address set for Tuesday could come too late.

One senior Republican aide told Fox News there may be 300 lawmakers already on record against the use-of-force resolution in the House. The resolution was formally introduced in the Senate on Friday, with a vote there expected next week. The aide said the feeling among Republicans is the president should have delivered a major address this week, the "critical week" to change minds on the Hill.

Instead, the president traveled to the G-20 summit in St. Petersburg, Russia. Though he won early support from House Speaker John Boehner and other congressional leaders before leaving, 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.

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"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."

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.

Obama announced the Tuesday address while speaking toward the close of the G-20 summit in Russia. He reiterated that the Assad regime's alleged use of chemical weapons last month is a "threat to global peace and security" and must be met with a military response.

"I will make the best case that I can to the American people as well as to the international community to take necessary and appropriate action," Obama said.

The president was 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."

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.

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

"I was elected to end wars, not start them," he said. But he stressed that any U.S. involvement in Syria would be "limited." The president said that if the Rwandan genocide were happening now, "it probably wouldn't poll real well" either.

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.

Meanwhile, emerging videos are stoking concerns about the nature of the opposition that the U.S. would inevitably be helping should the U.S. strike Assad. Though there are moderate wings of the opposition that the Obama administration would like to support, some are worried about the risk of more extreme factions jockeying for control in the event of a power vacuum.

One video, obtained by The New York Times, purported to show Syrian rebels executing seven shirtless prisoners.

There’s also the concern of retaliation. The Wall Street Journal reported on Friday that the U.S. intercepted an order from the Iranian government to militants to attack U.S. interests in Iraq if there is a strike on Syria.

Fox News' Ed Henry and Wes Barrett contributed to this report.