Would a Senate endorsement alone give President Barack Obama sufficient political backing to launch a missile strike on Syria?

With flimsy support in the House, the Senate may be the best chance Obama has to get the thumbs-up from Congress that he’s looking for — though by no means is a favorable result in the Senate a slam dunk.

The president himself refused to say what he would do if Congress split or refused to authorize the use of force against Syria.

At a Friday news conference from the G-20 summit in Russia, Obama said he did not want to “jump the gun and speculate, because right now, I’m working to get as much support as possible.”

However, White House Deputy National Security Adviser Tony Blinken told NPR on Friday morning that the president would likely not act without Congress’ approval.

“The president, of course, has the authorization to act, but it’s neither his desire nor his intention to use that authority absent Congress backing him,” Blinken said. The adviser was not asked about a split verdict, however.

Still, Obama appears to be focusing most of his current lobbying efforts on the Senate. On Thursday, for example, he called five senators, and earlier in the week, he hosted pro-interventionist GOP Sens. John McCain of Arizona and Lindsey Graham of South Carolina at the White House. Of course, the Senate is also expected to vote before the House, with a possible test vote coming as soon as Sept. 11.

But while getting the 60 votes needed to beat back a possible filibuster in the Senate seems doable, rank-and-file House lawmakers on both sides of the aisle have expressed deep skepticism about the need to retaliate for the Syrian regime’s alleged use of chemical weapons against its own people. A majority of House members either have already come out against action in Syria or have indicated they are leaning against voting for a strike.

While many senators also remain skeptical, some of those who have expressed reservations appear to be looking for a reason to say “yes” to a possible strike. For example, Sens. Joe Manchin III, D-W.Va., and Heidi Heitkamp, D-N.D., are circulating a resolution that would give the Syrian regime 45 days to give up its chemical weapons or face unspecified retaliation. Failure of the Syrian regime to sign on to a treaty banning chemical weapons would lead to “all elements of national power” being considered by the U.S. government.

Supporters of military intervention have also been aggressively lobbying their fellow senators. Senate Intelligence Chairwoman Dianne Feinstein is among those warning of the broad foreign policy consequences of not rallying behind the president.

But even supporters, like Feinstein, acknowledge the lack of public support. The California Democrat, for instance, said Thursday that constituent calls to her office about Syria are clearly against her position.

“Every day, I get a report on what the calls are, where the calls are coming from, what the nature of the argument is, and there’s no question, what’s coming in is overwhelmingly negative,” Feinstein said.

But Feinstein said she still would be spending much of her time making sure that senators have as much information as possible about why a strike is needed.

“What I’m trying to do in specific is seeing that they have all the information they need. And that’s a big job in itself. So we will … keep doing that, and hopefully they will go to other briefings,” Feinstein said. “I mean, they can certainly be undecided, up to the vote, but, you know, there’s a moment of truth in all of this.”

As supporters of the president’s position, House GOP and Democratic leaders have been trying to influence their unconvinced rank and file and praised Obama’s announcement that he would address the American public on Sept. 10.

A spokesman for Speaker John A. Boehner said Friday that the Ohio Republican has “consistently said the president has an obligation to make his case for intervention directly to the American people.” Boehner earlier came out in favor of intervention in Syria, in retaliation for that regime’s alleged use of chemical weapons against its own people.

“Members of Congress represent the views of their constituents, and only a president can convince the public that military action is required,” Boehner spokesman Brendan Buck said. “We only hope this isn’t coming too late to make the difference.”

House Minority Leader Nancy Pelosi, D-Calif., sent a “Dear Colleague” letter Thursday arguing that the resolution approved by the Senate Foreign Relations Committee addressed many of the concerns House members have with a Syria attack, and she encouraged members to continue to suggest alternatives.

If Obama ultimately decides to strike with or without a unified Congress, the backlash from both parties could be intense.

“It would be very, very difficult for [Obama’s] presidency, his relationship with Congress. It would reinforce deep cynicism about the disconnect between how we conduct ourselves and what we value,” said freshman Rep. Beto O’Rourke, D-Texas.

“I have to think that he will respect our decision,” said O’Rourke, who says he will oppose the resolution.

Not every House Democrat thinks Obama’s reputation would be on the line.

“My decision will be based upon not the issue of credibility, and I wish we’d not hold that standard up,” another Texas Democrat, Rep. Sheila Jackson Lee, said on Thursday, adding that she was still deliberating her position. “I think America has shown itself to be credible. The president has showed himself to be credible. And I’m saddened that our memory fails us and this is a president that captured Osama bin Laden.”

Emma Dumain, Matt Fuller and Steven T. Dennis contributed to this report.