WASHINGTON — Despite a late scramble by members of Congress on Sunday night, the federal government shutdown barreled into its third day on Monday — the most consequential, as the first weekday affecting hundreds of thousands of government employees across the country. The shutdown is the first in modern times when a single party controlled all the Washington levers of power.

During an unusual Sunday legislative session, Republicans planned a procedural Senate vote designed to pave the way for a compromise measure funding the government in the short term. But while the senators had initially hoped to hold the vote at 1 a.m. Monday, the office of Senate majority leader Mitch McConnell subsequently said a deal had not been forged, and he delayed the vote until noon on Monday.

Even as a bipartisan group of about 20 senators struggled Sunday to craft the compromise short-term spending deal, both sides spent much of the day publicly digging into their respective positions.

Democrats continued to hold out for a short-term budget deal that would also protect from deportation immigrants brought to the United States illegally as children. Republicans continued to maintain that immigration should not be in the mix in budget talks and that Democrats should not be rewarded for their hardball tactics.

McConnell told reporters Sunday that he preferred that Congress pass a clean government funding bill and resolve immigration issues in a separate debate next month. Democrats would almost certainly not agree to this plan, which would rob them of their most potent leverage.

Estimates say almost 1 million civilian federal workers will be temporarily unemployed starting Monday.

Trump’s frustration at Congress’s inability to end the shutdown boiled over Sunday morning when he called on the Senate to use the “nuclear option’’ to eliminate filibuster rules and allow a budget to pass on a simple majority.

The president’s demand via his favorite medium, Twitter, renewed the intense scrutiny over his struggles to lead Republicans past their impasse with Democrats.

“The president’s position is clear: We will not negotiate on the status of unlawful immigrants while Senator [Chuck] Schumer and the Democrats hold the government for millions of Americans and our troops hostage,’’ said a statement Sunday from White House press secretary Sarah Huckabee Sanders.

Democrats late Sunday said they did not yet have a deal that would win their support. And with Trump’s White House having sent mixed signals on its policy preferences in the past, trust seemed at an ebb on all sides.

Republican Senator Lindsay Graham took the unusual step of criticizing members of Trump’s staff Sunday.

“Their staff has been unreliable’’ on these issues, Graham told reporters. “We need a reliable partner.’’

That extraordinary rebuke echoed Schumer’s charge Saturday that “negotiating with President Trump is like negotiating with Jell-O.’’

In a message to supporters, Trump continued his shutdown blame game, stating in a press release that Democrats are putting “illegal immigrants over American citizens’’ because they are seeking to extend protections for young undocumented immigrants.

Democrats responded by pointing out that Trump himself has previously expressed sympathy for that population of immigrations.

Democrats also seized on Trump’s “nuclear option’’ demand, saying that the president was once again showing a lack of negotiating prowess and accusing him of seeking to change Senate rules rather than live up to his boast of being an expert dealmaker.

“We are a government that can only operate if the majority party, the governing party, accepts and seeks compromise,’’ said Schumer. “The majority, however, has forgotten the lessons of the founding fathers. They have shown that they do not know how to compromise.’’

In a statement, McConnell said he opposes Trump’s idea on the filibuster.

Questions over which party will get blamed for the shutdown of many government services dominated Washington talk shows Sunday.

The current standoff has its roots in September, when Trump revoked President Obama’s DACA program, which protected from deportation nearly 800,000 young undocumented immigrants brought to the United States as children. Trump’s rationale was Obama’s executive order creating the program was illegal and Congress should pass a law authorizing it.

At the time, many warned that Trump’s decision would force too much on the already crowded plate of Congress. Now, five months later, the issue of whether or not to reinstate DACA is central to the budget deadlock and government shutdown, which began Friday at midnight.

The bipartisan group of senators has sought to craft a compromise short-term spending plan that they could present to their respective leadership teams.

Any compromise would have to address Republican plans to secure the border along with Democratic hopes to protect the immigrants who were covered by DACA.

The Trump administration has demanded major changes to the country’s legal immigration system and full funding for Trump’s proposed border wall between the United States and Mexico.

Those new demands torpedoed a bipartisan proposal that looked to have been on track to passage just weeks ago. The measure, which was negotiated by 20 Republican and Democratic senators, would have kept the government open, solved challenges such as DACA and expiring funding for the Children’s Health Insurance Program, and given the administration money for the border wall.

Reports have said Trump was ready to make the deal, but anti-immigration forces in the White House such as policy adviser Stephen Miller and chief of staff John Kelly later convinced the president that he should be tougher.

“As long as [White House aide] Stephen Miller is in charge of negotiating immigration, we are going nowhere. He’s been an outlier for years,’’ Graham said.

Ryan said Democrats should agree to the temporary funding measure and then have a separate policy fight around immigration.

“We are waiting for the Senate Democrats to open the government back up,’’ Ryan said on CBS’s “Face the Nation’’ Sunday morning.

The White House released a set of photos showing Trump “working in the White House’’ over the weekend, along with a list of congressional officials with whom the president and his top staffers were in regular contact on Sunday.

But some mocked the photos the White House released, particularly one in which Trump is dramatically posing with a phone next to his ear.

“Not sure who, if anyone, was on the other end of that call, but it wasn’t Senate Democrats,’’ tweeted Massachusetts Senator Ed Markey. “We stand ready to make a deal but @realDonaldTrump needs to do his job and negotiate in good faith.’’

Local impact

Visitors attempting to see many US-run tourist sites in the Boston area left disappointed, but Old Ironsides remained open. B1.

Herndon can be reached at astead.herndon@globe.com.