WASHINGTON — President Trump’s denunciation of the $900 billion coronavirus relief deal drove a wedge through the Republican Party on Wednesday, drawing harsh criticism from House Republicans and threatening the delivery of unemployment checks, a reprieve on evictions and direct payments to struggling Americans.

His four-minute video on Tuesday night demanding significant changes to the bill and larger direct stimulus checks also complicated his party’s push to hold the Senate with victories in two runoff races in Georgia next month. The Republican candidates he pledged to support went from campaigning on their triumphant votes for the relief bill to facing questions on Mr. Trump’s view that the measure was a “disgrace.”

Their Democratic rivals appeared to turn a liability into a political advantage 13 days before the election on Jan. 5, agreeing with the president’s demand for $2,000 direct payment checks and calling for Republicans to accede to his wish. Speaker Nancy Pelosi and top Democrats prepared to move forward on Thursday with new legislation that would provide the $2,000 checks, daring Republicans to break with the president and block passage of the bill in the House.

But the effect on struggling Americans was perhaps the most profound: With no deal signed by the president, some unemployment programs are set to run out this week, and several other critical provisions are to end this month. The uncertainty that Mr. Trump injected into the process came at a perilous moment for the economy, as consumer spending and personal incomes resumed their slides.

“Does the president realize that unemployment benefits expire the day after Christmas?” an exasperated Senator Mark Warner, Democrat of Virginia and one of the key negotiators of the package, wrote on Twitter.

It is not clear whether Mr. Trump, who is furious at congressional Republicans who have acknowledged his defeat, would actually veto the package. But given how late it is in the 116th Congress, even refusing to sign it could ensure that the bill dies with the Congress on Jan. 3 and must be taken up all over again next year.

The 5,593-page spending package would not only provide relief but also fund the government through September. With his threat, the president raised the prospects of a government shutdown beyond Monday and also jeopardized a promise of swift relief to millions of struggling Americans and businesses.

Mr. Trump on Wednesday also made good on his promise to veto a major defense policy bill, in part because it directed the military to strip the names of Confederate generals from bases. That sets up a showdown for next week; when the House returns on Monday for the override vote, it could also vote on another stopgap spending bill to prevent government funding from lapsing.

Before the turmoil, Treasury Secretary Steven Mnuchin had promised that $600 direct payments from the pandemic relief bill could be distributed as early as next week; that is an untenable timeline without Mr. Trump’s signature. The end to two expanded unemployment programs the day after Christmas could push nearly five million people into poverty virtually overnight, according to an estimate from researchers at Columbia University.

Some state labor departments — which administer both state and federal unemployment benefits — are already preparing for the end of the programs because of the delay in reaching an agreement, meaning some jobless workers may temporarily lose their benefits all the same because many states will not be able to reverse course in time to avoid a lapse in payments.

Frustration with Mr. Trump boiled over on Wednesday during a private conference call of House Republicans who had loyally stood by the president; many of them had joined a baseless lawsuit to try to overturn the results of election. Representative Kevin McCarthy of California, the Republican leader, told members that he had spoken to the president and that he had not yet committed to a veto of the bill.

But Mr. McCarthy conceded, “This bill has been tainted,” according to one person on the call.

In his videotaped statement on Tuesday, Mr. Trump accused lawmakers of putting aid for foreign governments before the needs of the American people.

Some lawmakers on the call complained about the pork projects in the spending measure; others chimed in to challenge the characterization of the projects as pork, and one longtime House Republican vented generally about voter perceptions of the package after Mr. Trump’s scathing critique.

“I don’t know if we recover from this,” said Representative Virginia Foxx, Republican of North Carolina, according to three officials on the call. “We will have a hell of a time getting this out of people’s head.”

Representative Don Bacon, Republican of Nebraska, said Mr. Trump had thrown House Republicans under the bus, according to a person on the call. In a statement afterward, Mr. Bacon said, “I stand by what I said,” adding that “the Covid supplemental is a good compromise, and the president should take it.”

Focused first on the general election and then on baseless attempts to reverse its outcome, Mr. Trump has largely been sidelined from the negotiations, instead dispatching Mr. Mnuchin as his main emissary.

During a private meeting with top Republicans and top Democrats to discuss the emerging relief deal, Ms. Pelosi at one point pressed Mr. Mnuchin, on speaker phone in her conference room, four times to articulate the president’s position on direct payments. “Come on, Steven,” she said when he refused to say, according to one person familiar with the meeting, who disclosed it on the condition of anonymity.

Now, in undercutting the negotiations that Mr. Mnuchin led for the White House and throwing passage of the $2.3 trillion package into limbo with little warning to top Republicans on Capitol Hill, Mr. Trump has increased the likelihood that the party will bear the brunt of the blame for the continuing delay in providing relief to Americans.

The coronavirus relief package would provide the first significant infusion of federal aid since April, when Mr. Trump signed a $1.4 trillion government funding package. In rejecting it, the president would also derail some of his own priorities tucked into the measure, like funding for his wall at the southwestern border, funding for the Pentagon and an agreement to ban surprise medical bills, which his administration had previously urged lawmakers to pass. A number of the funding provisions Mr. Trump singled out in the catchall omnibus also aligned with requests he had made in his own budget proposal.

Republicans would again be forced to choose between their party’s leadership in Congress — Mr. McCarthy and Senator Mitch McConnell of Kentucky, who helped negotiate the final details of the stimulus deal — and a president known to savage anyone he views as disloyal.

Mr. Trump’s demands also provided a political gift to Democratic leadership, who have faced criticism for accepting a $900 billion relief package with $600 direct payments after months of pushing multiple multitrillion-dollar proposals that would have set the payments to twice that amount.

With the House set to convene on Christmas Eve in a so-called pro forma session — typically a brief meeting that requires one lawmaker to be present and lasts for a few minutes — Democrats plan to bring up a stand-alone bill that would provide for $2,000 direct payments to American families and ensure that the omnibus is signed. Should that request fail without unanimous consent, Democrats plan to formally bring the bill up for a vote on Monday, according to two people familiar with the plans.

“Just when you think you have seen it all, last night, the president said that he would possibly veto the bicameral agreement negotiated between Republicans and Democrats,” Ms. Pelosi wrote in a letter to Democratic colleagues. She noted that if Mr. Trump “truly wants to join us in $2,000 payments,” he should urge Republicans to allow the unanimous consent request to go through.

In a letter to House Republicans late Wednesday, Mr. McCarthy indicated that the party would put forward its own unanimous request to revisit the portion of the omnibus spending bill that funds the State Department and other related agencies. He charged that Democrats had “conveniently ignored the concerns expressed by the president” about those funds. (That legislation had also secured the support of 128 Republicans when it passed the House on Monday.)

But the Democratic argument could prove particularly potent in Georgia, where the Democratic challengers in the two runoff races have locked arms to call on their Republican opponents, Senators David Perdue and Kelly Loeffler, to support the $2,000 direct payments.

Jon Ossoff, Mr. Perdue’s Democratic opponent, posted to Twitter a series of memes and videos mocking the $600 payments supported by Republican leadership.

The Rev. Dr. Raphael G. Warnock, Ms. Loeffler’s opponent, said in a statement, “As I’ve said from the start, the Senate should have acted on this months ago, and support for Georgians should have been far greater.” He continued: “Donald Trump is right, Congress should swiftly increase direct payments to $2,000. Once and for all, Senator Loeffler should do what’s best for Georgia instead of focusing on what she can do for herself.”

But some Republicans, including the most outspoken House conservatives, are continuing to lobby Mr. Trump to veto the legislation.

“Republicans are in grave danger if they continue to do the very swamp crap the president ran against,” Representative Chip Roy of Texas said in an interview, noting that it made it harder to run against Democrats as socialists when “establishment Republicans are passing massive spending and programs they then complain about.”

Mr. Roy said that if Mr. Trump vetoed the measure, lawmakers could devise a bill extending paycheck protection for businesses, hash out a compromise on unemployment benefits and direct payments, and pass legislation keeping the government open until the new Congress decided on spending levels next year. But few other lawmakers said they believed Congress would reconvene to craft a new measure during the holidays.

Michael Steele, the former chairman of the Republican National Committee and a critic of the president, noted that the foreign aid proposals to which the president was objecting were proposed by his own administration.

“The Republicans are getting punked again by the guy they shilled for, who does not care about their interests or any principle they stand for,” Mr. Steele said. “He made a four-minute video in the White House ranting about things his own administration did, and meanwhile some mom is trying to figure out how she can avoid eviction and get Christmas presents under the tree for her kids. That’s the heartbreaking part.”

Republicans in the two chambers were already at odds over the election results.

Many of the Senate Republicans are ready to move on from the Trump era while House Republicans, including the top leadership, signed on to a brief supporting a Texas lawsuit in hopes that the Supreme Court would overturn the results.

Mr. McConnell has tried to shut down the prospect of blocking the Electoral College results in the Senate next month, but House Republican leaders have not done anything in public to discourage hard-liners from trying such a move in the Democratic-controlled chamber. After Senator John Thune of South Dakota, the No. 2 Republican, told reporters this week that such an effort “would go down like a shot dog” in the Senate, Mr. Trump tweeted on Tuesday: “South Dakota doesn’t like weakness. He will be primaried in 2022, political career over!!!”

Reporting was contributed by Jonathan Martin from Washington, Ben Casselman and Nicholas Fandos from New York, and Rick Rojas from Atlanta.