House Speaker John Boehner of Ohio listens as President Barack Obama speaks to media in the Cabinet Room of the White House in Washington, Sept. 3, 2013, before a meeting with Congressional leaders to discuss the situation in Syria. (Carolyn Kaster/AP)

The aborted Capitol Hill debate on military action against Syria put President Obama and House Speaker John Boehner in a rare place — on the same side. But each found himself sharply at odds with lawmakers of his own party.

As Washington turns its attention to critical domestic issues this week, the turbulent political environment facing the nation’s leaders was put in sharp relief Sunday when opposition by Democratic lawmakers cost Obama his preferred candidate for chairman of the Federal Reserve, former economic adviser Lawrence H. Summers.

Summers’s forced withdrawal — an unprecedented insult to the president by members of his own party — was just the latest reminder of how both Obama and Boehner are facing questions about the strength of their leadership and whether they can avert a government shutdown or debt default that could significantly harm the economy.

Although a surprise Russian diplomatic proposal — to place Syria’s chemical weapons under international control — has reduced the urgency for a congressional vote authorizing military action, lawmakers say the leaders remain hampered by sharp partisan divisions and intraparty conflicts.

“It’s almost as though it was the end of traditional power,” Rep. James P. Moran (D-Va.), a fierce Obama supporter, said of rank-and-file resistance to the president and the speaker. “I’ve been here for 20 years, and I’ve never seen so much of a repudiation of the conventional sources of power in the legislative or executive branch.”

“It portends for a much more chaotic fall,” he said.

The most pressing issue is forging an agreement to keep the government open past Sept. 30, when a funding measure expires. Boehner (R-Ohio) is struggling to gain the support of enough Republicans to endorse his budget strategy, the latest sign of the speaker’s weakened hold over his conference.

The results of that effort will have implications for a more important challenge next month, when Congress must raise the federal debt ceiling or risk an unprecedented default by the federal government.

But Obama, whose position on Syria was all but certain to be rejected, has problems within his own party. On the domestic front, some House Democrats are questioning his decision not to take a harder line in the upcoming debate against the deep spending cuts known as sequestration.

With declining public support, the president also must fend off GOP attacks on his signature health-care law, the Affordable Care Act, as his administration prepares to launch a centerpiece of the effort, online insurance marketplaces, in just two weeks.

In a series of events, beginning Monday morning with a Rose Garden speech, Obama will pivot from Syria to pressing for a deal to keep the government open and raise the debt ceiling. Analysts say the government might run out of money to pay all bills as soon as Oct. 18.

But as the president makes a public push, Boehner and House Majority Leader Eric Cantor (R-Va.) will be working their own members to generate support for a bill keeping the government open. Polls show that Americans will resoundingly blame the GOP if the government shuts down Oct. 1.

A solution has proved elusive. Last week, Boehner and Cantor advanced a plan that would have kept the government open through mid-December while allowing rank-and-file Republicans to cast a symbolic vote against Obama’s health-care law.

Conservative Republicans, however, said the strategy was an obvious trick that would neither slow implementation of the law nor reduce government spending. The intensity of the opposition forced the GOP leaders to put off a vote.

“Leadership brought out a plan they thought would work, and some members kind of said no,” said Rep. Mike Simpson (R-Idaho), a Boehner ally. “So it’s kind of like sending leaders back to the drawing board and telling them, ‘Think again.’ ”

It was not the first time rank-and-file Republicans have rejected Boehner’s approach to legislating. Boehner, with 233 Republicans in his majority caucus, can afford fewer than 20 defections from his own ranks without being forced to seek Democratic votes if he wants to pass important legislation. Yet on seven key votes this year, a bloc of nearly 50 conservatives has opposed his position a majority of the time.

This time may prove the hardest. Democrats say they are absolutely against the main Republican demands: a delay or defunding of the health-care law, and further cuts to domestic spending.

Although GOP leaders say they may be able to get just enough votes to get through the Sept. 30 deadline without a shutdown, they do not yet see a way to find agreement to raise the debt ceiling. Obama says he will not negotiate on the debt limit, and some members expect this time will be worse than previous clashes.

“It’s Groundhog Day in the House, but it’s Groundhog Day coming up on default and shutdown,” said Rep. Peter Welch (D-Vt.). “The House is dysfunctional. The question is whether in the next couple of weeks it will actually disintegrate.”

While the divisions among the Republicans run deeper and are more acrimonious, several key Democrats have significant concerns about the White House’s approach to this fall’s budget strategy.

Aides say Obama is open to a short-term budget agreement that would keep sequestration in place. The position has outraged some Democratic lawmakers who say that the spending cuts are undermining key programs and that Democrats must take a hard line against them.

“I don’t agree with the White House. I think the White House is making a mistake, and I’ve told them so,” said the No. 2 House Democrat, Rep. Steny H. Hoyer (Md.). “They’re going to lock in that number.”

Hoyer said he is pushing House Democrats to demand a spending bill that scales back the automatic across-the-board cuts.

“I’m advising my members that it is time for us to take a stand,” he said. “Every time we’ve voted in a compromise with Republicans, we have made the economic picture of our country worse and we’ve undermined the growth of jobs and the economy.”

Other lawmakers are supportive of the White House, noting that defense spending is in line for a deeper cut under the sequestration deal than domestic agencies, putting pressure on Republicans to find a way to soften the spending reductions.

Summers’s decision to withdraw Sunday as a candidate for the Fed post is the clearest example of Obama’s struggle to maintain support of his own caucus. In recent days, liberal Democrats had erupted in opposition to Summers after a summer making a case against the man Obama was openly defending and privately hoping to nominate.

An open question going into these domestic debates is how much the president’s back-and-forth in recent weeks over whether to strike Syria has weakened him. On Sunday, Rep. Mike Rogers (R-Mich.), the chairman of the House Intelligence Committee, questioned the president’s leadership ability.

“The Syria plan has been confusing at best over the last two years,” he said on CNN’s “State of the Union.” “Last week, it was more confusing to the American people and more confusing to members of Congress about our national security interests. The president couldn’t quite close that deal.”

Obama, in an interview with ABC’s “This Week” broadcast Sunday, defended his approach. While acknowledging that it has been uneven, he said it has produced the right results, forcing the Syrian regime to agree to turn over its chemical weapons.

“Folks here in Washington like to grade on style. And so had we rolled out something that was very smooth and disciplined and linear they would have graded it well, even if it was a disastrous policy,” Obama said. “. . . I’m less concerned about style points. I’m much more concerned about getting the policy right.”