Millions of Americans are set to lose their unemployment coverage after Saturday as President Trump resisted signing a sweeping $900 billion aid package until lawmakers more than tripled the size of relief checks, putting the fate of the measure in limbo.

Mr. Trump’s resistance to signing the bill risks leaving millions of unemployed Americans without crucial benefits jeopardizes other critical assistance for businesses and families set to lapse at the end of the year and raises the possibility of a government shutdown on Tuesday.

The president blindsided lawmakers this week when he described as “a disgrace” a relief compromise that overwhelmingly passed both chambers and was negotiated by his own Treasury secretary. He hinted that he might veto the measure unless lawmakers raised the bill’s $600 direct payment checks to $2,000, and Mr. Trump, who was largely absent from negotiations over the compromise, doubled down on that criticism on Saturday while offering little clarity on his plans. A White House spokesman declined to indicate what the president intended to do.

“I simply want to get our great people $2000, rather than the measly $600 that is now in the bill,” Mr. Trump said on Twitter Saturday, a day he continued to dedicate many of his posts to falsehoods about the election. “Also, stop the billions of dollars in ‘pork.’”

If the president does not sign the $2.3 trillion spending package, which includes the $900 billion in pandemic aid as well as funding to keep the government open past Monday, coverage under two federal jobless programs that expanded and extended benefits will lapse after Saturday, meaning millions of unemployed workers will lose them.

The consequences of such a delay are dire, economists, policy experts and lawmakers said, particularly as the United States’ economic recovery continues to sputter and the pandemic ravages the country. Some warned that any resolution at this point may be too late for families who will have lost their only lifeline shielding them from the brunt of the pandemic’s economic toll and will further burden overwhelmed state unemployment agencies waiting for guidance on how to enact the legislation.

“Foreclosures, hunger, homelessness, suicide,” said Michele Evermore, a senior policy analyst for the National Employment Law Project, a nonprofit workers’ rights group. “There will be very permanent things that happen to people that can’t be fixed by a check-in three weeks.”

Even if the legislation becomes law before the end of the 116th Congress on Jan. 3, the delay will have guaranteed a temporary lapse in unemployment benefits because states will not be allowed to restart benefits until the first week of January. The delay has also effectively reduced the scope of the extension and expansions in the relief bill because they are still scheduled to end in mid-March. A provision in the bill adding $300 a week to unemployment benefits would now last for 10 weeks, instead of the intended 11.

“That’s a significant amount of uncertainty for the tens of thousands of residents throughout the state that has been dependent on all this,” said Max Reiss, a spokesman for Gov. Ned Lamont of Connecticut. “They’re basically being told, ‘You’re going to have to wait a little longer.’ But what they’re waiting for, we basically don’t know. And that is an unfair position to put people in when we were so close to the finish line days ago.”

“I’m not sure we have a choice but to look to the new administration,” he added. “But at that point, we’re almost a month from where we are now and that would mean a lot of suffering for residents who are waiting for support.”

“This abdication of responsibility has devastating consequences,” he said in a statement on Saturday.

The unsigned 5,593-page bill is now waiting at Mar-a-Lago, the Florida estate where Mr. Trump is spending the holidays. In addition to providing direct payments and reviving lapsed benefits, the legislation would allocate billions of dollars for the distribution of vaccines and to support struggling small businesses, schools, hospitals, airlines and transit agencies across the country.

After spending time with Mr. Trump on Christmas Day, Senator Lindsey Graham, Republican of South Carolina, offered support for the president’s push for larger direct payments in the spending legislation and for his veto of a military policy bill this week because it did not repeal a legal shield for social media companies. Mr. Trump has cited the absence of a repeal as one reason for his veto, which lawmakers in both parties have said should not be addressed in such a bill.

“Both are reasonable demands, and I hope Congress is listening,” Mr. Graham said on Friday.

Before Mr. Trump’s insistence that the legislation increases relief checks to Americans, Steven Mnuchin, the Treasury secretary, had promised direct payments could be sent as early as next week — a timeline that was also now in jeopardy.

But many of those receiving the jobless benefits were worried about losing them so abruptly and what that would mean for their finances in the new year.

Hicham Oumlil, a self-employed fashion designer in Brooklyn, said that he and his wife, a furloughed interior designer, are both set to lose nearly $600 a week, leaving the couple and their 7-year-old son without a source of income. Having paid less than half of his rent each month for the past three months, Mr. Oumlil, 48, said he feared falling deeper into debt if the relief bill did not become law. If they have dependent children, they would also get $600 for each child. People with incomes just above these levels would receive a partial payment that declines by $5 for every $100 in income.

“Our livelihoods have been shattered,” he said. “The government is showing no leadership. I am floored by what is currently happening in Congress.”

After House Republicans blocked a Democratic effort to unilaterally increase the $600 direct payments to $2,000 per adult, top Democrats plan to hold a roll-call vote on the measure on Monday when the full House is present. Lawmakers could also potentially approve a stopgap funding bill to keep the government running.

“As the economy continues to falter, folks are hanging on by a thread and desperately need this federal relief to continue so they can afford basics like food, medicine, diapers, phone bills, and housing,” said Representative Richard E. Neal of Massachusetts, the chairman of the House Ways and Means Committee. “It is underhanded and cruel for the president now to refuse to sign it into law and potentially end this brutal year by inflicting even more pain and suffering on families in need.”

The president’s implicit threat to reject the spending package roiled Republicans on Capitol Hill, who said Mr. Trump’s rebuke of the legislation had taken them by surprise after they overwhelmingly supported the bill. (In fact, many of Mr. Trump’s complaints were about measures in the government funding bills that were in line with White House budget requests.)

The direct payments were kept at half of the original $1,200 amount approved in the $2.2 trillion stimulus law in March, partly to accommodate a Republican reluctance to spend more than $1 trillion, and there is little indication a majority of Republicans would support such an increase.

“I hope the president looks at this again and reaches that conclusion that the best thing to do is to sign the bill,” Senator Roy Blunt, Republican of Missouri, told reporters this week. “I think that would be to the president’s advantage if we were talking about his accomplishments rather than questioning decisions late in the administration, but, again, Congress has very little control over what the president can say.”The comments are particularly fraught for Senators Kelly Loeffler and David Perdue in Georgia, who are both facing runoff races in early January that will determine control of the Senate.

The campaign for Jon Ossoff, Mr. Perdue’s Democratic opponent, asked TV stations on Saturday to remove one of Mr. Perdue’s ads highlighting his support for the bill, accusing him of taking “an unwarranted victory lap on Covid-19 relief that does not exist.”