WASHINGTON — A group of Senate Republicans is threatening to delay action on a spending bill needed to avert a lapse in federal funding on Friday unless it also bans enforcement of the Biden administration’s vaccine-and-testing mandate for large employers, heightening the threat of a government shutdown.

With Congress lagging behind on finalizing the dozen annual spending bills needed to keep the government running, there is broad acknowledgment that lawmakers will need to pass a stopgap measure this week to stave off a shutdown.

But just two days before funding is set to lapse, Democrats and Republicans remain at odds over how long the temporary measure should stretch into 2022 and other details. Congressional leaders in both parties have downplayed the chances of a shutdown, but they conceded that the funding deadline has increased the leverage of senators pressing their own individual agendas.

“If every member of this chamber used the threat of a shutdown to secure concessions on their own interests, that would lead to chaos for the millions and millions of Americans who rely on a functioning government,” said Senator Chuck Schumer, Democrat of New York and the majority leader.

“It’s up to the leaders to make sure there’s not a shutdown — I’m making sure, and I think Leader McConnell wants to try to make sure, too,” he added, referring to Senator Mitch McConnell, Republican of Kentucky and the minority leader.

On Tuesday, Mr. McConnell flatly said, “We won’t shut down.”

Still, the vaccine mandate-related objections have raised the prospect of at least a temporary lapse in funding, presenting the first hiccup for Senate Democrats in a chaotic month, as they juggle efforts to fund the government, raise the debt ceiling, complete a hulking military policy bill and enact their marquee $2.2 trillion domestic policy legislation — all before Christmas Day.

“We will not support — and will use all means at our disposal to oppose — legislation that funds or in any way enables the enforcement of President Biden’s employer vaccine mandate,” a dozen Republican senators, led by Senator Roger Marshall of Kansas, wrote last month in a letter to Mr. Schumer. It was unclear on Wednesday how many of the signees would hold firm in blocking the unfinished legislation.

The House Freedom Caucus, the right flank of the House Republican conference, wrote their own letter on Wednesday asking Mr. McConnell to use “all procedural tools at his disposal to deny timely passage” of the legislation.

The House could vote as early as Wednesday on a short-term spending bill that keeps the government open through at least late January, but aides warned it could be delayed as lawmakers spent the morning haggling over the end date.

“There is no interest in shutting the government down,” said Representative Rosa DeLauro, Democrat of Connecticut and the chairwoman of the Appropriations Committee, on Wednesday. “We will get to an endpoint.”

Because the stopgap bill maintains existing funding, effectively freezing in place spending levels negotiated with the Trump administration and a Republican-controlled Senate in 2020, Democrats are pressing to make it as short-lived as possible. But Republicans have pushed to extend the measure longer.

“I’d like February, March would suit me — April, May,” said Senator Richard C. Shelby of Alabama, the top Republican on the Appropriations Committee. “I think it gives us more time to seriously sit down.”

Lawmakers were also debating additional spending provisions, including additional funding for Afghan refugees and a provision averting billions of dollars in cuts to Medicare, subsidies and other programs. But even if an agreement is reached, the Senate would require unanimous support to waive a number of procedural steps and swiftly take up the legislation before the Friday deadline.

Without unanimous agreement, the process could drag through the weekend, forcing a brief shutdown. Senate Republicans, with the strong backing of House Republicans, have threatened to prolong the debate unless the bill prohibits funding for a mandate that all large employers require their workers be vaccinated against the coronavirus or submit to weekly testing.

“I have long said that I am not particularly invested in the timing of a given vote — whether it occurs a few hours earlier or a few hours later,” Senator Ted Cruz, Republican of Texas, told reporters. “But I think we should use the leverage we have to fight against what are illegal, unconstitutional and abusive mandates.”

Mr. Marshall previously offered an amendment in September to an earlier stopgap bill that would have barred funds from going toward the implementation and enforcement of the mandate, but it failed in the evenly divided Senate.

The mandate, which the Biden administration had said would go into effect in January, has become ensnared in court challenges. Last month, a federal appeals court kept a block on it in place and declared that the Occupational Safety and Health Administration had overreached its authority in issuing it.

Some Republicans appeared wary of forcing a shutdown, however temporary, over the issue.

“A shutdown is just a useless pathway,” said Senator Shelley Moore Capito, Republican of West Virginia.

Democrats criticized Republicans on Wednesday for threatening to shutter the government over a policy that is aimed at stemming the spread of the pandemic.

“The fact that they want to walk right up to a government shutdown over a public health issue should frighten the American public,” said Representative Pete Aguilar, Democrat of California. “That’s exactly what they’re advocating here.”