WASHINGTON — The idea to funnel cash directly to millions of Americans to help them weather the economic disaster ravaging the globe amid the coronavirus pandemic got its jump-start not from the liberal left, but from a more unlikely source: the most conservative reaches of the Republican Party.

Recognizing a looming calamity for anxious people who are losing their incomes because of a government-ordered shutdown of much of the nation’s economy, some senators who would normally be expected to block a direct federal payout to the poorest Americans, potentially costing $500 billion or more, instead got behind it early.

The idea is at the heart of an emerging economic stabilization package whose price tag was swelling beyond $1 trillion on Saturday as top Republicans and Democrats and Trump administration officials drew closer to an agreement that could be enacted within days.

“I believe we are poised to deliver the significant relief that Americans need with the speed that this crisis demands,” Senator Mitch McConnell, Republican of Kentucky and the majority leader, said in a statement Saturday night, before a test vote on Sunday meant to pave the way for passage of the package on Monday.

In a round of feverish private negotiations that unfolded on Capitol Hill and included Steven Mnuchin, the Treasury secretary, the largest sticking point appeared to be the scope of jobless aid that should be included. With Democrats pressing to broaden the scope of unemployment insurance, Republicans had agreed to a significant expansion of the program that would cover almost all wages and offer benefits to those who are self-employed and people whose hours had been reduced, according to two people familiar with the emerging deal who insisted on anonymity to discuss details that were still being finished.

But there was little disagreement about sending cash payments to Americans as part of the extraordinary government rescue, with Republicans leading the charge. It was a striking populist turn for a party that has been dominated for decades by small-government activists, including some who rose to political prominence in the wake of the Wall Street bailout and are now determined to steer federal help to the most vulnerable of their constituents.

“This is a public health crisis of the likes that has not been seen in a century,” said Senator Tom Cotton, a deeply conservative Republican from Arkansas and one of the chief proponents of getting cash in the hands of hurting Americans as quickly as possible. “Our government at every level has to take responsibility for caring for our people and caring for their health and their material well-being as well.”

It was hardly the expected Republican response, given staunch party resistance to the Obama administration’s 2009 stimulus program after the 2008 financial crisis and a Republican history of rescuing big businesses and then leaving it to those employers to take care of the rest.

But there was Mr. Cotton on “Fox & Friends” last week, pushing the idea of a quick cash infusion to counter the economic devastation of the coronavirus outbreak. A few hours later, Senator Mitt Romney, Republican of Utah, proposed on Twitter that “every American adult should immediately receive a one-time check for $1,000.” The idea was first met with skepticism and even incredulity.

But as it became clear there was bipartisan opposition to President Trump’s push for a payroll tax holiday, Mr. Mnuchin got onboard and the cash idea quickly transformed from pipe dream to reality, to the centerpiece of Senate Republicans’ roughly $1 trillion rescue plan. The optics were jarring, since it is Republicans who usually accuse Democrats of being too quick to throw taxpayer money around.

“Senate Republicans want to put cash in Americans’ hands,” Mr. McConnell said on the Senate floor as colleagues of both parties worked behind closed doors to hammer out the details of the economic stabilization plan.

Not everyone was as enthusiastic about the cash payments. Some Republican colleagues balked, Democrats had reservations about the scope and distribution of the payments and conservative fiscal watchdog groups were aghast.

David McIntosh, the head of the free-market Club for Growth, said Republicans seemed to have borrowed the idea from Andrew Yang, the former Democratic presidential candidate who proposed a $1,000 universal monthly income. The idea, Mr. McIntosh noted, was ridiculed by Republicans just a few weeks ago.

“It is panic-driven — panic on Capitol Hill,” Mr. McIntosh said. “There is no indication it would work or make a difference. They are throwing up any idea.”

Under the Senate Republicans’ original bill, individuals could receive one-time checks of a maximum of $1,200 or $2,400 for married couples, in addition to $500 a child. Those earning more money would get a bigger check, and the payment would phase out for those earning more than $75,000, ending entirely for taxpayers with more than $99,000 in income or families earning $198,000. The initial Senate measure would also reduce the payments to $600 for people with no income tax liability but at least $2,500 in earnings.

But those provisions came under attack from lawmakers in both parties and were quickly overhauled in the bipartisan negotiations, in favor of a program that would send the full amount to those at lower income levels. Senator Josh Hawley, Republican of Missouri and another ultraconservative, was among those pushing for that change.

Republican resistance to the cash payments came from Senator Lindsey Graham of South Carolina, who said it was more practical to use unemployment insurance to supplement income. Other Senate Republican said privately that they were not convinced that the cash payout would be all that effective, but they were not about to jump in front of a moving legislative train and look as if they were denying relief to struggling constituents.

On the Democratic side, progressives were pushing for more generous payments on a monthly basis during the crisis and higher eligibility levels. But Democratic leaders were reluctant to face accusations that they had pushed for checks going to the affluent. Speaker Nancy Pelosi and Senator Chuck Schumer of New York, the minority leader, also wanted to make sure due consideration was given to other Democratic priorities, such as a significant expansion of unemployment insurance and aid to states and hospitals.

Some Democrats acknowledged they were taken aback by the willingness of Republicans to embrace such spending.

“I’m more worried about the deficit than most Republicans,” said Representative Tom Malinowski, Democrat of New Jersey, who favors targeted cash payments.

Senate Republicans were determined to go big with the economic assistance plan after Mr. McConnell allowed the Trump White House and congressional Democrats to largely take the lead on the first two emergency relief packages, leaving some of his party’s senators frustrated. The strategy opened the door to expansive legislative proposals as Senate Republicans sought to put their own stamp on the pandemic response.

A spokeswoman for Mr. Romney said that given his business background, he was aware of the potential hardship for sidelined employees and focused on cash assistance to speed aid, rather than trying to rely on a more complicated system of existing unemployment programs and tax breaks.

“He kind of just put it out there without a lot of detail, knowing there would be a conversation about it,” said Liz Johnson, Mr. Romney’s spokeswoman. “Consensus grew around it literally overnight.”

This isn’t the first time the government has sent out checks under a Republican president. President George W. Bush did so twice in 2001 and again in 2008 during that years’s economic downturn, to mixed reviews. But this is the first time since the inception of the Tea Party movement, which stirred a backlash in 2010 against government intervention and bailout programs.

The Club for Growth endorsed Mr. Cotton in his first Senate run in 2014, and Mr. McIntosh said he was surprised by the senator’s strong support of the cash payment plan, since he usually backs “what will work.”

His prominent support is a risk to Mr. Cotton, who has been discussed as a possible Republican presidential candidate in 2024, if the proposal is later found to be wasteful and ineffective. But he seems confident of the approach based on his understanding of economic conditions in his home state and the threat posed to virtually every American by the economic halt.

“Growing up where I did, folks were frequently working paycheck to paycheck,” he said. “I certainly don’t hear the perspective you would hear if you were a rich guy in New York or Washington or another big city and everyone you know works at a big financial firm or a Fortune 500 company.”

Emily Cochrane and Jim Tankersley contributed reporting.

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