With a government shutdown looming in less than three weeks, Republican House leaders conceded Wednesday that they have yet to muster enough votes to approve a plan to keep federal agencies open.

A vote on the measure, set for Thursday, was postponed until at least next week after conservatives balked, demanding that any deal to fund the government include a provision to cut off funding for President Obama’s signature health-care initiative.

Unless Congress acts, the government will shut down Oct. 1. The Treasury also faces a potential default as soon as Oct. 18, according to independent estimates. House Speaker John A. Boehner (R-Ohio) has said he wants to avoid a shutdown and a default. But deep divisions within Republican ranks have left Boehner scrambling for a strategy that the vast majority of his caucus would embrace.

Democrats worry that the GOP-controlled House will be unable to act — leaving Washington barreling toward economy-rattling deadlines for the third straight year.

As GOP leaders struggled to build support for a plan backed by Boehner, members of the ­conservative Republican Study Group put forward their own proposal at a closed-door meeting.

Some floated the idea of increasing the debt ceiling, as Obama and the Democrats want, to avoid a default by the nation as well as more funding for government agencies, ending some of the deep federal spending cuts known as sequestration. Such an offer, they said, would have to be accompanied by an agreement to delay for one year the full implementation of Obama’s health-care law.

GOP leaders are pushing their original proposal, which would fund the government at current levels through Dec. 15, while haggling with conservatives for a broader resolution. Boehner’s measure includes a resolution to defund the Affordable Care Act, commonly called Obamacare. But the legislation is structured to allow the Senate to vote down that provision and send the underlying bill to the president for his signature, which would avoid a government shutdown.

Although several Republicans called the situation “fluid,” some rank-and-file lawmakers made clear Wednesday that they would not accept Boehner’s terms.

“Wouldn’t it be ironic if the government shuts down because our leadership won’t offer a bill that Republicans will vote for? That’s what happened this week,” said freshman Rep. Thomas Massie (R-Ky.), one of the leading agitators pushing to defund the health-care law, even if it means shutting down the government.

Obama has rejected any attempts to negotiate over the legislation.

“We will not accept anything that delays or defunds Obamacare,” White House press secretary Jay Carney said Wednesday. “Harming the economy to refight old political battles, to refight a battle that was waged and ended when Congress passed the law, the president signed the law, [and] the Supreme Court upheld the law is not in the interest of the American middle class.”

The gridlock among House Republicans came as the top four leaders in Congress plan to huddle Thursday morning to try to find a way forward on the pressing fiscal deadlines: Oct. 1, when funding is set to expire for the government, and Oct. 18, when the Treasury is likely to begin running out of measures to keep borrowing and begin the process that could lead the nation to default on its nearly $17 trillion in debt.

A report by the Bipartisan Policy Center this week found that the Treasury may be able to stretch funding into early November. But the longer such efforts continued, the more global financial markets would drift toward chaos, the center said.

On Tuesday, Boehner and House Majority Leader Eric Cantor (R-Va.) introduced a plan to keep government agencies funded through Dec. 15, at an annualized rate of $986.3 billion that would leave in place the sequester budget cuts.

The plan quickly unraveled as conservatives said it was insufficient — with a tea-party-aligned nonprofit group accusing Boehner of having “betrayed” the cause. Democrats also joined the fray.

“Republican leaders spent all week pledging to jam through a temporary funding measure that defunds the Affordable Care Act, wreaks havoc on Medicare and extends the life of the Republican sequester,” House Minority Leader Nancy Pelosi (Calif.) said Wednesday. “But division in their own ranks scuttled this latest gambit.”

In a recurring theme of Boehner’s leadership, the opposition from Democrats left him fishing for votes entirely among the 233 Republicans in the House. But dozens quickly opposed the plan, leaving House leaders well shy of the majority needed to pass the bill.

Despite the criticism from their ranks, senior Republicans — who have witnessed numerous implosions in the past two years on everything from spending legislation to tax measures to the farm bill — said the situation has not reached those depths.

“It’s not time to panic,” Rep. Harold Rogers (Ky.), chairman of the House Appropriations Committee, told reporters.

Cantor spent an hour Wednesday at the Republican Study Committee meeting, listening to others’ ideas but not offering any, lawmakers said.

Some came away optimistic, given that many conservatives said they might be willing to go along with the leadership’s original proposal if they can craft a longer-term plan to defund the health-care law through the fight over the debt ceiling.

“The emotion has been creatively channeled,” said Rep. Steve Southerland II (R-Fla.), a conservative who represents the massive class of 2010 before leadership.

Several Republicans pointed to the mere suggestion among some conservatives that they might be open to greater spending in a compromise as a sign that common ground could be found.

“Maybe this thing could work,” said Rep. John Campbell (Calif.), a senior member of the study committee.

That tactic was based on leveraging a health-care delay, which they suggested would create its own savings that would more than offset increased funding for federal agencies. David Plouffe, Obama’s former top political adviser, compared continuing efforts to block the health-care law to “a fairy tale on par with those waiting for unicorns.”

White House officials said they would not agree to Republican proposals that they offset an increase in defense spending with deeper cuts to other domestic programs. One factor working in the administration’s favor: The 10-year sequester will slice more deeply into defense spending than domestic agencies next year, raising concerns among some Republicans.

A public opinion poll released Wednesday suggested that Republicans and the White House are on weak ground in the coming budget fight. The CNN-ORC International poll found that one-third of Americans would blame Obama for a government shutdown, while 51 percent would blame Republicans.

But support for the health-care law is also dropping, the poll showed, with 39 percent of Americans supporting most of Obamacare, sharply down from 51 percent at the beginning of the year.

Lori Montgomery, Zachary A. Goldfarb, Ed O’Keefe and Billy Kenber contributed to this report.