WASHINGTON (NewsNation Now) — U.S. Senate Republican leader Mitch McConnell on Wednesday said a Democratic bill to raise coronavirus relief checks to $2,000 from $600 was unlikely to clear the Senate anytime soon, likely killing an effort to boost the aid that was championed by President Donald Trump.

McConnell said on the Senate floor that a bill passed by the Democratic-controlled House of Representatives, which sought to meet Trump’s demands for bigger checks, “has no realistic path to quickly pass the Senate,” and McConnell’s proposed alternative approach of loading up the bill with other White House priorities appeared destined to fail.

The roadblock set by Senate Republicans appears insurmountable, even as pressure builds to approve the bigger checks. Trump wants the Republican-led chamber to follow the House and increase the checks from $600 to $2,000 for millions of Americans, and tweeted “$2000 ASAP!” early Wednesday. A growing number of Republicans, including two senators in runoff elections on Jan. 5 in Georgia, agree. But most GOP senators oppose more spending, even if they are also wary of disagreeing with Trump.

Increasing the $600 checks to $2,000 would cost $464 billion, according to the Joint Committee on Taxation, which prepares cost estimates for legislation before Congress.

Senators were back at it Wednesday after McConnell blocked a vote Tuesday on the standalone bill passed by the House, but his new bill — which includes the formation of a commission to investigate the 2020 election as well as a complicated repeal of big tech liability protections — does not have enough support to pass. McConnell filed the new legislation late Tuesday linking the president’s demand for bigger checks with two other Trump priorities.

With a new Congress due to be sworn into office on Sunday following November’s election, McConnell’s remark suggested the legislation that passed the House on Monday would simply expire.

“What we’re seeing right now is Leader McConnell trying to kill the checks — the $2,000 checks desperately needed by so many American families,” Senate Democratic leader Chuck Schumer said.

McConnell said the $2,000 checks were not targeted and would go to some people who do not need them.

Republican Senator John Cornyn told reporters that he thought it unlikely that Congress would act to increase the checks given McConnell’s remarks.

Asked if he expected Republicans to face political blow-back, Cornyn said: “No, not in any normal world,” noting that Congress had already approved trillions of dollars in relief for an economy battered by the pandemic.

House Democrats led passage of the original standalone bill, 275-134, with 44 Republicans joining almost all Democrats on Monday for a two-thirds vote of approval.

No votes are scheduled in the Senate on either the House-passed measure supporting Trump’s $2,000 checks or McConnell’s new version. With time running out, it almost ensures neither bill will pass.

The showdown over the $2,000 checks 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 has prevented action on another priority — overturning Trump’s veto on a sweeping defense bill that has been approved every year for 60 years. The Senate held a procedural vote Wednesday afternoon, voting 80-12 to begin an official debate on whether to override the president’s veto.

Trump has criticized Republican leaders for the stonewalling, finding rare common cause with the Democrats pushing them to act. Leading Republicans warned that the GOP’s refusal to provide more aid as the virus worsens will jeopardize next week’s Senate election in Georgia.

“The Senate Republicans risk throwing away two seats and control of the Senate,” said Newt Gingrich, the former congressional leader, on Fox News. He called on Senate Republicans to “get a grip and not try to play cute parliamentary games with the president’s $2,000 payment.”

House Speaker Nancy Pelosi said, “These Republicans in the Senate seem to have an endless tolerance for other people’s sadness.”

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.

Meanwhile, Treasury Secretary Steven Mnuchin said some of the $600 payments were being sent by direct deposit to Americans’ bank accounts Tuesday night. Paper checks will begin to go out Wednesday.

Congress had settled on smaller $600 payments in a compromise over the big, year-end relief bill Trump reluctantly signed into law.

The debate over the size and scope of the year-end package — $900 billion in COVID-19 aid and $1.4 trillion to fund government agencies through September — is potentially the final confrontation before the new Congress is sworn in Sunday.

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.

Reuters and The Associated Press contributed to this report; reporting by Susan Cornwell and David Morgan; additional reporting by Trevor Hunnicutt, Lisa Lambert, Jeff Mason and David Brunnstrom.