WASHINGTON (AP) — Senate Majority Leader Mitch McConnell on Tuesday blocked Democrats' push to immediately bring President Donald Trump's demand for bigger $2,000 COVID-19 relief checks up for a vote, saying the chamber would “begin a process” to address the issue.

Pressure is mounting on the Republican-led Senate to follow the House, which voted overwhelmingly on Monday to meet the president's demand to increase the checks from $600 as the virus crisis worsens. A growing number of Republicans, including two senators in runoff elections on Jan. 5 in Georgia, have said they will support the larger amount. But most GOP senators oppose more spending, even if they are also wary of bucking Trump.

The outcome is highly uncertain heading into the rare holiday-week session.

“We should not adjourn until the Senate holds a vote,” Senate Democratic leader Chuck Schumer said as he made a motion to push it toward a vote.

McConnell, who has said little publicly on Trump's request, objected but gave almost no indication of his plans ahead.

“The Senate will begin a process," the GOP leader said. He said he plans to bring the president's demand for the $2,000 checks and other remaining issues “into focus.”

The showdown has thrown Congress into a chaotic year-end session just days before new lawmakers are set to be sworn into office for the new year. It's preventing action on another priority — overturning Trump's veto on a sweeping defense bill that has been approved every year for 60 years.

The president's last-minute push for bigger checks deeply divides Republicans, who are split between those who align with Trump’s populist instincts and those who adhere to what had been more traditional conservative views against government spending. Congress had settled on smaller $600 payments in a compromise over the big year-end relief bill Trump reluctantly signed into law.

Liberal senators led by Bernie Sanders of Vermont who support the relief aid are blocking action on the defense bill until a vote can be taken on Trump's demand for $2,000 for most Americans.

The two GOP senators from Georgia, David Perdue and Kelly Loeffler, announced Tuesday they support Trump's plan for bigger checks as they face Democrats Jon Ossoff and Raphael Warnock in runoff elections that will determine which party controls the Senate.

“I’m delighted to support the president,” said Perdue on Fox News. Loeffler said in an interview on Fox that she, too, backs the boosted relief checks.

Trump tweeted his demands ahead of Tuesday's Senate session: "$2000 for our great people, not $600!"

The House vote late Monday was a stunning turn of events. Just days ago, during a brief Christmas Eve session, Republicans blocked Trump's sudden demand for bigger checks as he defiantly refused to sign the broader COVID-19 aid and year-end funding bill into law.

As Trump spent days fuming from his private club in Florida, where he is spending the holidays, dozens of Republicans calculated it was better to link with Democrats to increase the pandemic payments rather than buck the outgoing president and constituents counting on the money. Democrats led passage, 275-134, but 44 Republicans joined almost all Democrats in approval.

House Speaker Nancy Pelosi declared, “Republicans have a choice: Vote for this legislation or vote to deny the American people the bigger paychecks they need."

The showdown could end up as more symbol than substance if Trump's effort fizzles out in the Senate and may do little to change the COVID-19 relief and federal spending package Trump signed into law Sunday.

That package — $900 billion in COVID-19 aid and $1.4 trillion to fund government agencies — will deliver long-sought cash to businesses and individuals and averted a federal government shutdown that otherwise would have started Tuesday.

Together with votes this week to override Trump’s veto of a sweeping defense bill, it's potentially one last confrontation between the president and the Republican Party he leads as he imposes fresh demands and disputes the results of the presidential election. The new Congress is set to be sworn in Sunday.

Rep. Kevin Brady of Texas, the ranking Republican on the Ways and Means Committee, acknowledged the division and said Congress had already approved ample funds during the COVID-19 crisis. “Nothing in this bill helps anybody get back to work,” he said.

Aside from the direct $600 checks to most Americans, the COVID-19 portion of the bill revives a weekly pandemic jobless benefit boost — this time $300, through March 14 — as well as the popular Paycheck Protection Program of grants to businesses to keep workers on payrolls. It extends eviction protections, adding a new rental assistance fund.

Americans earning up to $75,000 will qualify for the direct $600 payments, which are phased out at higher income levels, and there's an additional $600 payment per dependent child.

President-elect Joe Biden told reporters at an event in Wilmington, Delaware, that he supported the $2,000 checks.

Trump's sudden decision to sign the bill came as he faced escalating criticism from lawmakers on all sides over his eleventh-hour demands. The bipartisan bill negotiated by Treasury Secretary Steven Mnuchin had already passed the House and Senate by wide margins. Lawmakers had thought they had Trump's blessing after months of negotiations with his administration.

The president's defiant refusal to act, publicized with a heated video he tweeted just before the Christmas holiday, sparked chaos, a lapse in unemployment benefits for millions and the threat of a government shutdown in the pandemic. It was another crisis of his own making, resolved when he ultimately signed the bill into law.

In his statement about the signing, Trump repeated his frustrations with the COVID-19 relief bill for providing only $600 checks to most Americans and complained about what he considered unnecessary spending, particularly on foreign aid — much of it proposed by his own budget.

While the president insisted he would send Congress “a redlined version” with spending items he wants removed, those are merely suggestions to Congress. Democrats said they would resist such cuts.

For now, the administration can only begin work sending out the $600 payments.

Most House Republicans simply shrugged off Trump’s push, 130 of them voting to reject the higher checks that would add $467 billion in additional costs. Another 20 House Republicans — including Minority Leader Kevin McCarthy of California, a Trump confidant — skipped the vote, despite pandemic procedures that allow lawmakers to vote by proxy to avoid travel to the Capitol. McCarthy was recovering at home from elbow surgery, his office said.

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Colvin reported from West Palm Beach, Florida. Associated Press writers Bill Barrow in Atlanta and Ashraf Khalil in Washington contributed to this report.