It's hard to say no to a president.

Top lawmakers were summoned to the White House shortly after President Obama announced that he would seek congressional approval for a military strike against Syria. And most of them, Republican and Democrat alike, exited the West Wing in an unusually agreeable mood.

In quick succession, House Speaker John Boehner, R-Ohio, and House Minority Leader Nancy Pelosi, D-Calif., announced that they would support a resolution authorizing a U.S. military strike against President Bashar Assad's regime in retaliation for its use of chemical weapons against Syrian citizens.

"This is behavior outside the circle of civilized human behavior and we must respond," Pelosi said.

Boehner was just as direct. "This is something that the United States, as a country, needs to do," he said.

A short time later, Boehner's top deputy, House Majority Leader Eric Cantor, R-Va., announced that he too would back an attack.

The support of the bipartisan trio of House leaders improves the chances that Obama will get the 218 House votes and 60 Senate votes he needs to authorize a strike soon after Congress returns from summer recess on Sept. 9.

But it's hardly a done deal.

Senate Majority Leader Harry Reid, D-Calif., supports the military strike and has privately told aides he believes there are enough votes in the Senate to pass it. If the Republican-led House approved the resolution first, it would make it easier for the Senate to approve it.

But with dozens of lawmakers still to be won over, including a sizable anti-war faction on the Left and an increasingly non-interventionist group of conservatives on the Right, the House will be a hard sell.

No one knows this better than Boehner, who has seen several major initiatives killed on the House floor by varying combinations of Democrats and an unruly faction of Tea Party Republicans.

A top Boehner aide described the effort to pass the resolution as "an uphill battle."

And Boehner doesn't want to be blamed if the resolution fails.

Shortly after he announced his support for a strike, Boehner's aides issued a statement saying that the speaker was still leaving it to the administration to win over other House Republicans.

Obama can likely count on many establishment Republicans for support, including Boehner, his closest allies and the top Republicans on the committees overseeing national security. But the president will have a much harder time winning votes from the dozens of House GOP newcomers with Tea Party roots, who don't want the United States expending time, money or military effort on something that does not directly impact U.S. security.

Among the doubtful is Rep. Renee Ellmers, R-N.C., who was elected along with about 50 other Republicans in the 2010 Tea Party wave election that focused on reducing the nation's staggering debt.

"I don't think we're economically strong enough to commit to any military action," Ellmers told the Washington Examiner. 'I'm worried about our military as a whole and the commitment we'd be making ... even if the initial plan is a short-term strategic hit."

On the Democratic side, Pelosi plans to help Obama win votes for the resolution and he'll likely pick up moderates and those in his own party who believe it is imperative to support the president.

Pelosi issued a "Dear Colleague" letter recently stipulating that the United States must "respond to the Syrian government’s unspeakable use of chemical weapons."

But Pelosi and Obama will face resistance from a faction of staunchly anti-war Democrats, many who were elected a half-dozen years ago out of public opposition to the wars in Iraq and Afghanistan.

The path to passage for both parties will lie in the details of the resolution. House and Senate lawmakers are working on a measure that would limit the scope and time frame of military involvement from what the Obama administration first proposed. Among the likely provisions is one prohibiting the president from putting U.S. troops on the ground in Syria.

By making it clear a military strike won't turn into a repeat of Iraq and Afghanistan, Rep. Gerry Connolly, D-Va., a moderate, said, "we can get a majority in the House and the Senate."

Congressional Correspondent Tim Mak contributed to this report.