President Trump said Tuesday that his administration is “going big” with a $1.2 trillion rescue plan — including a proposal for direct payments of $1,000 or more to most Americans — for an economy rocked by the COVID-19 pandemic.

The White House announced the plan as airlines, hotels, retailers and other businesses nationwide seek relief in the wake of an outbreak that has brought the country to a standstill.

Treasury Secretary Steven T. Mnuchin said after an urgent afternoon meeting with Senate Republicans that the White House proposal had grown from $850 billion earlier in the day.

“We put a proposal on the table that would inject $1 trillion into the economy,” Mr. Mnuchin said at the Capitol. “It is a big number. This is a very big situation in this economy. The president wants to put money in the economy now.”

The White House proposes issuing means-tested checks of at least $1,000 to most Americans, to be delivered in late April, totaling $250 billion. A second round of direct payments would go out four weeks later if Mr. Trump hasn’t ended the national emergency declaration by that time.

In addition, the plan would provide $300 billion for small business loans, $200 billion in stabilization funds and $300 billion in deferred tax payments to the IRS. Included in the total would be $59 billion for the airline industry.

The size of the proposal reflected the administration’s growing alarm at the scope of the pandemic’s impact across the country.

Mr. Mnuchin announced that the IRS will allow most Americans to delay paying their taxes for 90 days, although he encouraged those who can to file on or before April 15 to do so, so that they don’t lose out on their tax refunds.

Several major retailers, including Macy’s, Nordstrom and Apple, announced they are closing for several weeks. They are joining companies in the travel, tourism and hospitality industries that have been brought to nearly a standstill by the outbreak.

The United Auto Workers labor union is asking Detroit’s three major automakers to close their factories for two weeks to keep its members safe from the coronavirus that causes COVID-19. Ford, General Motors and Fiat Chrysler haven’t agreed to the request, which would idle 150,000 union workers.

Fiat Chrysler, Ford, Volkswagen and Daimler AG have closed their European factories.

Airlines said they have lost more than 1 million passengers in the first two weeks of March compared with the same period last year. The administration has banned most flights from Europe for the next 30 days.

Mr. Trump met Tuesday at the White House with hotel executives, who said their businesses, employing 5 million people, are reeling.

“Our industry has been impacted in a devastating way,” Christopher Nassetta, president and CEO of Hilton, told the president. “I’ve been doing this for 35 years, never seen anything like it. In a few days or a week, we will probably be running 10 to 15% occupancy. The bulk of our hotels in the major cities are closing as we speak.”

Stocks stabilized Tuesday after the market’s worst point drop in history. Major indexes recovered more than 5% on the news of the administration’s plan and the Federal Reserve’s offer of help for small businesses. The Dow Jones Industrial Average rose 1,049 points, or 5.2%, to close at 21,237. The tech-heavy Nasdaq was up more than 6.2%, and the S&P 500 rose nearly 6%. The indexes lost about 12% on Monday, with the Dow falling nearly 3,000 points, on concerns about the pandemic.

Aside from the rising cost of the administration’s rescue plan, the suggestion of sending checks to Americans raised objections in conservative circles, such as at the Club for Growth.

“Some Republicans have embraced cash stipends for families so they can afford to buy food and pay bills,” the advocacy group said Tuesday. “This policy should be opposed. It provides a giant transfer payment system that imposes net costs on the economy. Relief for families should be provided through existing government welfare programs and the enhanced unemployment insurance program.”

As for the eye-popping cost of the administration’s rescue plan, Mr. Mnuchin said saving the economy is more important than rising budget deficits.

“Congress right now should be concerned about the American workers and small business,” he said. “Interest rates are incredibly low, so there’s very little cost of borrowing this money. We’ll fix the deficit. This is not the time to worry about it. This is the time that hardworking Americans are impacted by government decisions. That’s when the government has to step up to put money into the economy.”

Some conservative Republican senators said they supported or were at least open to sending checks directly to workers. Sen. Josh Hawley of Missouri said it was “exactly the right thing to do.”

Sen. Todd Young of Indiana said he is focused on “what is most helpful to the individual American worker who is unable to work.”

Although lawmakers in both parties agree on the need for significant federal action, the path forward in Congress isn’t clear. Senate Majority Leader Mitch McConnell, Kentucky Republican, said Republican lawmakers need to agree with the White House on a proposal before negotiating with House Speaker Nancy Pelosi, California Democrat, and others in her party.

Mrs. Pelosi, whose proposal doesn’t mesh with a $750 billion relief plan from Senate Minority Leader Charles E. Schumer, New York Democrat, doesn’t envision aid for hotels or airlines.

Any relief that emerges for workers and businesses would be added to a bill approved by the House last week to provide paid sick leave and free virus testing, which is estimated to cost taxpayers about $105 billion.

It all began on Feb. 25 with Mr. Trump’s proposal to spend $2.5 billion to help states speed up access to testing. That measure grew to $8.5 billion by the time the president signed it.

On Tuesday, Mr. Trump emphasized the growing need to speed aid to workers who are being sidelined by the pandemic.

“I don’t want people losing their jobs or not having money to live when they were doing very well just four weeks ago,” Mr. Trump said at the White House. “So we’re going big.”

The president had been pushing for a payroll tax cut through the end of the year, but he acknowledged that the impact of such relief would be felt more slowly.

“Payroll tax is one way, but it does come over a period of months,” Mr. Trump said. The president said he wants to “do something that gets money to them as quickly as possible.”

“Obviously, some people shouldn’t be getting checks with $1,000,” he said.

Mr. Mnuchin said the president wants checks to be issued within two weeks, which seems unlikely.

“Americans need cash now,” Mr. Mnuchin said.

He suggested there would be an income limit for recipients. The threshold was still under discussion.

“We don’t need to send people who make a million dollars a year checks,” Mr. Mnuchin said.

He underscored the urgency.

“The president has instructed me we have to do this now,” he said. “This is no fault to American workers. For medical reasons, we are shutting down parts of the economy.”

He added that other sectors of the economy need help, too.

“This is worse than 9/11. For the airline industry, they’ve almost ground to a halt,” he said.

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