WASHINGTON – The House Monday passed some changes to the sweeping coronavirus relief bill to pave the way for a vote in the Senate as early as this week. If the Senate backs it, it will head to President Donald Trump's desk for his signature.

Which means the relief it promised millions of Americans, such as low-income pregnant women, home-bound seniors and workers who lose their jobs over the crisis would be freed up.

After another day of a free-falling stock market, Trump acknowledged earlier that the U.S. economy “may be” heading toward a recession because of the coronavirus.

Those who stand to benefit from the Families First Coronavirus Response Act, include:

Low-income mothers or mothers with young children who lose their jobs or are laid off due to the crisis.

Food stamp recipients who face the loss of their assistance because they lost their job to the coronavirus. The Supplemental Nutrition Assistance Program (SNAP) generally requires those receiving food stamps to be employed.

Food banks that serve economically struggling neighborhoods.

Health care workers whose exposure to the virus is supposed to be monitored and limited through a health standards developed by federal agencies.

House-bound seniors who rely on home delivery of meals through government programs.

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A procedural hiccup stalled relief

The measure had to overcome a snag.

The Families First measure was drafted, brought to the floor and passed 363-40 by the House in roughly 24 hours. That's a quick turnaround considering the political machinery of Congress that purposely keeps lawmakers from rushing legislation, even in times that demand urgent action.

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Technical issues connected to the already controversial portion guaranteeing paid sick leave for workers affected by the coronavirus crisis were discovered shortly after its passage, requiring a follow-up bill to fix what have been described by backers as minor problems.

The House passed those fixes Monday by "unanimous consent." A lengthier delay in the bill appeared possible after Rep. Louis Gohmert, a Texas Republican, said he couldn't back the technical corrections bill.

Gohmert later dropped his objections.

More issues add to the hold-up

Senate support for the bill grew after a briefing lawmakers had with the White House.

Some conservative senators expressed concerns about the impact of the sick leave provisions on small businesses.

Sen. Ron Johnson, R-Wis., said small firms could suffer major hardships if they are forced to "pay wages they cannot afford."

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Senate plots its course

As the House was fixing its bill, the Senate was examining possible changes to tackle the challenges the virus is posing to American families and the economy.

Utah GOP Sen. Mitt Romney said some of his colleagues are floating the option of adding additional measures to the House bill that would address other sectors of the economy.

“There’s some who think ‘no, no we'd better do phase three at the same time,’ because we may not, you know, be coming back if somebody gets the coronavirus or whatever happens,” he said. “Maybe we need to get phase three done before phase two is out the door.”

Other Republicans are wary of the paid leave for workers proposal, saying it could force some companies to lay off employees to be able to absorb the cost of the leave for illnesses and family care.

Johnson, the Wisconsin Republican, said he's worried not only about potential layoffs but also about “incentivizing people to not show up for work either and don't necessarily want to do that. You have to think this thing through in terms of what are the unintended consequences of good intentions."

“People are going to have to work. People do need to recognize the fact that this is not Ebola. This is not MERS. It's not quite the seasonal flu," Johnson said. "But we have to keep things in perspective and we got to keep our economy."

Other economic lifelines proposed

The administration already is working with Democrats on another relief bill to help cruise lines, airlines and other businesses that have been particularly hammered by the economic fallout from the virus. The airlines alone are seeking $50 billion in grants and loans to cover losses from coronavirus.

Senate Minority Leader Chuck Schumer, D-NY. has unveiled a proposal to spend $750 billion to address a number of sectors, including emergency child care for health care workers and first responders; medicine and food delivery systems for seniors, and assistance to keep public transportation running.

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“We will need big, bold, urgent federal action to deal with this crisis,” Schumer said. “The kinds of targeted measures we are putting together will mainline money into the economy and directly into the hands of families that need it most."

And Senate Majority Leader Mitch McConnell has his own list of broad priorities: more help for families dealing with financial challenges, aid to businesses hurt by the disruptions and shoring up the health care sector to prevent it from becoming overburdened.

“We must work with each other in the bipartisan spirit this moment demands and with the administration and the House to deliver results for our country,” the Kentucky Republican said.

Contributing: Bart Jansen, Nicholas Wu