WASHINGTON — Budget negotiations broke down Saturday — just days before the nation reaches its borrowing limit — as angry Republicans said that President Obama had rejected their latest offer.

“It’s now up to the Senate Republicans to stand up,” said Rep. Raul R. Labrador of Idaho after House Republicans left a closed-door meeting in the Capitol.

The message from Speaker John A. Boehner had been grim, Republicans said. John Carter described Obama as “acting like a royal president.”

“He’s still my way or the highway,” Carter said.

With House Republicans insisting that they have all but run out of options, attention now turns to the Senate, where Republicans have spent the past several days trying to gin up Democratic support for a proposal that they hope could reopen the government and extend the debt-ceiling through the end of January.

“The question is: What will Senate Republicans do, what will Senate Democrats do?” said Rep. Adam Kinzinger, R-Ill.

The answer to that question came shortly after noon: Senate Republicans blocked a Democratic proposal that would have extended the debt ceiling through the end of 2014, with no strings attached.

It was a near party-line vote — 53-45 — that derailed the Democratic measure in the Senate. The 53 votes were seven short of the 60 required to overcome Republican objections to considering the measure.

Although House Republicans — especially the more hard-line conservatives — remain reluctant to accept any proposal that comes out of the Democratic-controlled Senate, even if it has substantial Republican-backing, the question facing Boehner is whether he will be forced to put any Senate offering on the House floor for a vote.

With concern growing that global financial markets could be thrown into turmoil if Congress does not agree to raise the debt ceiling by Thursday, Republicans said they did not know whether Boehner would have enough support from his most conservative members to put a plan that passes the Senate up for a vote.

Many Republicans said that, however frustrated they were that the White House would not negotiate with them, they were just as dismayed with many of their own House colleagues, who would not back down from their demands that any deal include provisions to chip away at the president’s health care law.

“The problem here is that we don’t have a functioning majority,” said Rep. Nunes, R-Calif. “After three weeks of this, they’re still not figuring it out. I don’t know what it takes.”

The proposal House Republican presented to the White House late last week called for increasing the Treasury Department’s authority to borrow money through Nov. 22, but only if Obama agreed to more expansive talks about overhauling the budget.

But a breakdown in talks with the White House going into the weekend further soured an already tense relationship between House Republicans and the president. Rep. Aaron Schock, R-Ill., called the development “a total breakdown in trust.”

“You don’t tell the speaker, the majority leader, the majority whip, ‘We’re going to negotiate.’ Then they come and tell our entire conference, ‘We’re going to negotiate,’” he said. “And then 24-hours later, you recant.”

Prior to the vote, Sen. Harry Reid, the majority leader, said that, in the event the vote failed, he would consider executing a procedural maneuver known as a motion to recommit that would allow him to bring the plan to a vote again.

Sens. Susan Collins, R-Maine, and Joe Manchin III, D-W.Va., were also working to nail down the details of their own proposal, which would extend the debt ceiling through the end of January and include a stopgap spending measure to reopen the government and finance it through the end of March.

The 23-page plan would call for an immediate bipartisan conference of members of the House and the Senate to address broader budget concerns. Republicans hoped the conference would consider some of the cuts to social programs — like means-testing for Medicare benefits — that Obama has previously suggested could be options.

The proposal would also call for a two-year delay of a tax on medical devices unpopular with some Democrats, and would give government agencies more flexibility on how to carry out the existing across-the-board spending cuts known as sequestration.

When Collins presented a similar proposal to the president during a meeting on Friday, Obama called it “constructive.”

But some House Republicans remained skeptical that any Senate plan could pass muster in the Republican-controlled House. Rep. Thomas Massie, R-Ky., said the Republican conference remained “very united” and was unlikely to cede any ground as long as Obama continued to treat the standoff as “still a game.”

Reid warned that time was running out. “Each hour that goes by, we’re closer to a calamity for our country,” he said.

The Associated Press contributed to this report.