WASHINGTON — America is on the brink of a federal government shutdown after the House rejected a longshot effort to keep offices open as Republicans fight for spending cuts and stricter border security measures while  Democrats seek more spending and argue that cuts the GOP favors are too extreme.

Come 12:01 A.M. Sunday with no deal in place, federal employees will face furloughs, more than 2 million active duty and reserve military troops will serve without pay, and programs and services that Americans rely on from coast to coast will begin to face shutdown disruptions.

The Senate will be in for a rare Saturday session to advance its own bipartisan package that is supported by Democrats and Republicans and would fund the government for the short-term, through November 17.

Even if the Senate can rush to wrap up its work this weekend to pass the bill, which also includes money for Ukraine aid and American  disaster assistance, it won’t prevent an almost certain shutdown amid the chaos in the House. On Friday, a massive hard-right revolt left Speaker McCarthy’s latest plan to collapse.

“Congress has only one option to avoid a shutdown — bipartisanship,” said the majority leader in the Senate, Chuck Schumer.

Senate Republican leader Mitch McConnell echoed the sentiment, warning his own hard-right colleagues there is nothing to gain by shutting down the federal government. “It heaps unnecessary hardships on the American people, as well as the brave men and women who keep us safe,” Mr. McConnell said.

The federal government is heading straight into a shutdown that poses grave uncertainty for federal workers in states all across America and the people who depend on them — from troops to border control agents to office workers, scientists and others.

Families that rely on Head Start for children, food benefits, and countless other programs large and small are confronting potential interruptions or outright closures. At the airports, Transportation Security Administration officers and air traffic controllers are expected to work without pay, but travelers could face delays in updating their American passports or other travel documents.

Congress has been unable to fund the federal agencies or pass a temporary bill in time to keep offices open for the start of the new fiscal year Sunday in large part because Mr. McCarthy has faced insurmountable resistance from right-flank Republicans who are refusing to underwrite government as usual.

Mr. McCarthy’s last-ditch plan to keep the federal government temporarily open collapsed in dramatic fashion Friday as a robust faction of 21 hard-right holdouts opposed the package, despite steep spending cuts of nearly 30 percent to many agencies and severe border security provisions, calling it insufficient.

The White House and Democrats rejected the Republican approach as too extreme. The Democrats voted against it. The House bill’s failure a day before Saturday’s deadline to fund the government leaves few options to prevent a shutdown.

“It’s not the end yet; I’ve got other ideas,” a clearly agitated Mr. McCarthy told reporters as he exited the chamber.

Later Friday, after a heated closed-door meeting of House Republicans that pushed into the evening, Mr. McCarthy said he was considering options — among them, a two-week stopgap funding measure similar to the effort from hard-right senators that would be certain to exclude any help for Ukraine in the war against Russia.

Even though the House bill already axed routine Ukraine aid, an intensifying Republican resistance to the war effort means the Senate’s plan to attach $6 billion President Zelensky is seeking from Americans may have bipartisan support from Democrats but not from most of Mr. McCarthy’s Republicans.

Senator Paul of Kentucky, a Republican of Kentucky, is working to stop the Ukraine funds in the Senate package.

“We continue to work through trying to find a way out of this,” Mr. McCarthy told reporters. “There are no winners in a government shutdown, and I think that’s the best way forward, make sure the government does not shut down.”

The White House has brushed aside Mr. McCarthy’s overtures to meet with President Biden after the speaker walked away from the debt deal they brokered earlier this year that set budget levels.

On Friday, White House press secretary Karine Jean-Pierre said, “The path forward to fund the government has been laid out by the Senate with bipartisan support — House Republicans just need to take it.”

Catering to his hard-right flank, Mr. McCarthy had returned to the spending limits the conservatives demanded back in January as part of the deal-making to help him become the House speaker.

The House package would not have cut the Defense, Veterans or Homeland Security departments but would have slashed almost all other agencies by up to 30 percent — steep hits to a vast array of programs, services, and departments on which Americans have been depending.

It also added new border security provisions that would kickstart building the wall at the southern border with Mexico, among other measures. Additionally, the package would have set up a bipartisan debt commission to address the nation’s mounting debt load.

As soon as the floor debate began, Mr. McCarthy’s chief Republican critic, Representative Matt Gaetz of Florida, announced he would vote against the package, urging his colleagues to “not surrender.” Mr. Gaetz said afterward that the speaker’s bill “went down in flames as I’ve told you all week it would.”

Mr. Gaetz  and others rejecting the temporary measure want the House to keep pushing through the 12 individual spending bills needed to fund the government, typically a weeks-long process, as they pursue their conservative priorities.

Republican leaders announced later Friday that the House would stay in session next week, rather than return home, to keep working on some of the 12 spending bills.

Some of the Republican holdouts, including Mr. Gaetz, are allies of Donald Trump, who is Mr. Biden’s chief rival in 2024. The 45th  president has been encouraging the Republicans to fight hard for their priorities and even to “shut it down.”

The right wing, led by Mr. Gaetz, has been threatening Mr. McCarthy’s ouster, with a looming vote to try to remove him from the speaker’s office unless he meets the conservative demands. Still, it’s unclear if any other Republican would have support from the House majority to lead the party.

Late Friday on social media, Mr. Trump turned his ire to Mr. McConnell, complaining that the Republican leader and other GOP senators are “weak and ineffective” and making compromises with Democrats. He urged them, “Don’t do it.”