Senator Lindsey Graham called Trump's demand for $2,000 stimulus checks "reasonable," and urged Congress to listen.
Even if the president would sign the $900 billion stimulus into law as early as Sunday, millions of Americans could lose out on a week of $300 supplemental unemployment insurance.
The president-elect warned about the possibilities of unemployment benefits expiring as well as the economic impact that blocking the bill could have for small businesses.
"The best way out of this is for the president to sign the bill," Senator Roy Blunt told reporters.
The coronavirus relief deal remains in limbo over Christmas after House Republicans rejected President Donald Trump's demand for direct stimulus payments to be raised to $2,000.
The president traveled to Florida after threatening to tank a $900 billion stimulus package, risking a federal government shutdown and denying aid to millions of Americans during the pandemic.
"This president is holding up much needed help to them during some of the darkest days of American history," Representative Andy King said.
Additionally, the survey found 62 percent of Americans saying that the $600 checks were too small,
The block by Republicans was expected. However, it further underscored how at odds GOP lawmakers and the outgoing president are about stimulus spending, along with casting further doubt about the fate of the relief package.
An end to expanded unemployment programs on December 26 could push almost five million people into poverty, researchers estimate, unless additional relief is delivered.
House Speaker Nancy Pelosi has said she will put forward the proposal during a pro forma session on Thursday, a move that will test the loyalty of Republicans to the president.
"It will be up to Speaker Pelosi to decide if she wants to act on the behalf of the American people," House Minority Leader Kevin McCarthy (R-Calif.) wrote in a letter urging that foreign aid be "revisited" while Democrats rush to accept President Donald Trump's demand for $2,000 stimulus checks.
Georgia Senator David Perdue said he delivered "direct checks to Georgians" in a new advertisement released before President Donald Trump implied he would not sign a new economic stimulus bill unless the amount of direct payments was increased.
The coronavirus pandemic has roiled the markets, tossed most fiscal assumptions to the wind and driven the national debt to the highest level since World War II, as the government spent heavily to support the economy.
"I am asking Congress to amend this bill and increase the ridiculously low $600 to $2,000, or $4,000 for a couple," President Donald Trump said Tuesday.
"Mnuchin has been in the conversation for months with [congressional] leadership about how this was going to go," Bret Baier said.
"If the President truly wants to join us in $2,000 payments," House Speaker Nancy Pelosi wrote to fellow Democrats, "he should call upon Leader McCarthy to agree to our Unanimous Consent request."
Senator Amy Klobuchar suggested Trump's veto of the $900 billion coronavirus relief bill was purposely timed to come as most federal aid expires at the end of the year.
In a video, the president railed against the legislation for not providing enough in direct payments to Americans.
"President Trump is, as ever, erratic and all over the place, but on this point, tonight, he's right. $600 is a joke. They should send $2,000 checks to the American people right now because people are hurting," Georgia Democratic Senate candidate Jon Ossoff said on Tuesday.
A small minority of voters said the stimulus checks included in the latest relief bill were too large.
Democrats respond after President Trump labeled the $900 billion COVID-19 relief package "a disgrace" and called on lawmakers to raise direct payments from $600 to $2,000.
Treasury Secretary Steven Mnuchin said checks could arrive as early as next week.
The Democratic lawmaker from California said President Donald Trump should veto the stimulus package and took aim at the Treasury Secretary.
Critics are calling for cuts to the foreign aid provisions in this week's $1.4 trillion spending bill to fund more generous COVID stimulus checks for Americans.
The president threatened to veto the $900 billion COVID relief deal, calling on lawmakers to amend the bill to increase direct payments for most Americans from $600 to $2,000.
The president-elect said he would push for a third stimulus package next year.
Democrat leaders have gravitated to Trump's proposal, but it leaves Republican leaders in a quandary.
"Send the bill back, and we will put in the $2,000 we've been fighting for that your party has been blocking," tweeted Michigan Representative Rashida Tlaib.
"The bill they are now planning to send back to my desk is much different than anticipated. It really is a disgrace," Trump said Tuesday night.