Treasury Secretary Steven Mnuchin Steven Terner MnuchinLawmakers fear voter backlash over failure to reach COVID-19 relief deal United Airlines, unions call for six-month extension of government aid House Democrats plan to unveil bill next week to avert shutdown MORE and National Economic Council Director Larry Kudlow Larry KudlowMORE ran into Senate Republican opposition on key points of their economic rescue plan Tuesday when they outlined a multi-pronged proposal to keep the country from falling into a severe recession.

Many Republican senators feel frustrated they were largely cut out of negotiations with Speaker Nancy Pelosi Nancy PelosiSunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election Trump is betting big on the suburbs, but his strategy is failing 'bigly' Trump orders flags at half-staff to honor 'trailblazer' Ginsburg MORE (D-Calif.) that resulted in the speedy passage of a House bill estimated to cost more than $100 billion and President Trump Donald John TrumpUS reimposes UN sanctions on Iran amid increasing tensions Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Trump supporters chant 'Fill that seat' at North Carolina rally MORE says he will sign.

At a lengthy lunch meeting in the Russell Senate Office Building, Republican senators pushed back on two key points: distributing direct cash payments to Americans impacted by the coronavirus crisis and providing tens of billions of dollars in economic assistance to the ailing airline industry.

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Senior administration officials also heard criticism of the proposal Mnuchin negotiated with Pelosi to provide up to two-weeks of paid sick leave for the employees of small businesses.

Senate Judiciary Committee Chairman Lindsey Graham Lindsey Olin GrahamMomentum growing among Republicans for Supreme Court vote before Election Day Video of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral Warning signs flash for Lindsey Graham in South Carolina MORE (R-S.C.) objected to the administration decision to prioritize direct payments to Americans to juice up the faltering economy, which he called “money wasted.”

“It won’t help the economy just throwing money at a problem,” Graham said. “I don’t know why giving a thousand dollars on top of their paycheck makes any sense now because there’s no economy to participate in. I’d rather take that money and shore up health care systems.

“I said an extra thousand on top of your paycheck is money wasted right now,” he added. “I don’t think people are looking for a one time check from the government.”

The administration officials also ran into strong Republican pushback on a proposal to bail out the airline industry. U.S. airlines on Monday asked for $50 billion in economic assistance to make up for a precipitous drop in travel because of federal warnings and guidelines.

“A lot of us are against a bailout,” said Senate Appropriations Committee Chairman Richard Shelby Richard Craig ShelbySenate GOP eyes early exit Dems discussing government funding bill into February GOP short of votes on Trump's controversial Fed pick MORE (R-Ala.).

“I brought it up. I said loans, yes. They have a lot of collateral. Collateralize the loans, make sure they’re paid back,” he said.

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“As far as writing a check for bailout, I’d be totally against that,” he added.

Trump and Mnuchin doubled down on their call for economic relief of the airline industry earlier Tuesday.

“The airline industry will be in great shape,” Trump pledged.

“We’re going big,” he later added. “We don’t airlines going out of business. We don’t want people losing their jobs and not having money to live.”

Mnuchin told reporters Tuesday morning that the airlines are in danger of grinding to a “halt” and said “we want to maintain for critical travel the right to have domestic travel.”

Speaking to reporters after meeting with Senate Republicans, Mnuchin said that he’s had conversations “around the clock” with the CEOs of the top airlines.

"Airlines have a short-term liquidity issue,” he said. “We talked about it today; I've also spoken to the Speaker about that. So, [it’s] absolutely part of this: airlines, hotels, travel, other areas."

The Treasury secretary made clear that the president is prioritizing direct payments to Americans instead of cutting the payroll tax, a proposal Trump floated last week at a lunch meeting with Republicans.

Recognizing the difficulty of bringing his caucus together on a massive stimulus bill, Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellMomentum growing among Republicans for Supreme Court vote before Election Day Trump expects to nominate woman to replace Ginsburg next week Video of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral MORE (R-Ky.) announced Tuesday afternoon that he will set up three Senate GOP task forces to negotiate with the Treasury Department.

Mnuchin broke down his proposal to GOP lawmakers into three pieces: one focused on aid to small businesses; a second focused on helping American workers who miss paychecks because of the coronavirus; and a third centered on helping industries especially hard hit, such as the airlines.

Mnuchin and Kudlow made little push for the payroll tax cut Tuesday, said senators, a reflection that the idea has only mixed support in the Senate GOP conference and faces staunch Democratic opposition.

"I think this is something the White House is strongly inclined to," said Sen. Josh Hawley Joshua (Josh) David HawleyRenewed focus on Trump's Supreme Court list after Ginsburg's death What Facebook's planned change to its terms of service means for the Section 230 debate Republican Senators raise concerns over Oracle-TikTok deal MORE (R-Mo.), who said the proposal is now being considered "in lieu of the payroll tax cut."

"The more they look at the payroll tax cut, it just wouldn't deliver fast enough," he said.

Hawley, who supports the cash payment proposal, said he wants to calibrate cash payments to "family size and family need."

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Mnuchin called Hawley's proposal "a good idea."

Mnuchin and Kudlow also heard criticisms of the House-passed coronavirus relief bill, which the administration negotiated directly with Pelosi, leaving GOP senators on the sidelines.

Sen. Tom Cotton Tom Bryant CottonRenewed focus on Trump's Supreme Court list after Ginsburg's death Republicans call for DOJ to prosecute Netflix executives for releasing 'Cuties' Loeffler calls for hearing in wake of Netflix's 'Cuties' MORE (R-Ark.) raised his concern Tuesday over the decision to give employees of medium and small businesses affected by the coronavirus two-weeks of paid sick leave, which will be refunded to employers through tax credits.

Unlike Graham and some other colleagues, he wants the Treasury Department to immediately cut $1000 tax-rebate checks to every adult tax filer making less than $100,000 per year and $500 for each dependent.

“I think the paid leave provisions are too complicated. They won’t work fast enough. They don’t cover enough infected workers. They probably will even incentivize people for businesses to lay employees off and probably go bankrupt,” he said.

Cotton urged the Senate to “press pause” on the House-passed bill.

“We’re here all week long,” he said. “We should get it right on what the House sent us rather than just try to get it fast.”

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Cotton said a better solution is “to use the unemployment system to get checks out to any kind of affected worker, not just unemployed workers.”

Sen. Mike Braun Michael BraunPessimism grows as hopes fade for coronavirus deal McConnell shores up GOP support for coronavirus package Patient Protection Pledge offers price transparency MORE (R-Ind.) said he’s concerned about provisions in the House-passed bill that would funnel money in the form of loans of small businesses to help them ride through the crisis and avoid laying off workers.

Braun said the safety net of unemployment benefits should be relied on instead.

The Indiana senator added he raised objections with Mnuchin on “why can’t we use unemployment insurance” instead of “doing it through the payroll accounts of small businesses.”

Despite the pushback on the House-passed bill, McConnell announced Tuesday afternoon that he plans to bring it to the floor for a vote and then focus on additional stimulus by passing a “phase three” bill.

“We’re going to take up and pass the House bill,” he said. “Then Senate Republicans in conjunction with the administration are going to write a next bill.

McConnell said his advice to GOP critics of the House-passed legislation was to “gag and vote for it.”

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He said Senate Republican colleagues will have a chance to push their own proposals when they start negotiating with the administration on the next bill.

“We will then discuss with the Democrats what we can agree to pass, which of course will take 60 votes. The details of that obviously have not been determined yet.”

He also pledged the Senate will not leave town until it has passed both bills.

Mike Lillis contributed.