Lawmakers are already planning another round of legislation aimed at keeping companies flush with capital and millions of workers on payrolls amid the coronavirus pandemic, even after passing a $2 trillion relief bill this past week, the largest stimulus of its kind in U.S. history.

The Senate plans to be on recess until April 20, and the House will take an extended break as well, though members say they could return sooner depending on how the economy reacts in the next few weeks.

Businesses, trade associations and state governments are already jockeying for more federal relief, calling the package that President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE signed Friday a good “first step” but not enough to keep the economy on track if the coronavirus crisis extends beyond the end of April.

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Lawmakers in both parties say they expect discussions on a “phase four” coronavirus response bill in the weeks ahead as travel restrictions, social distancing and sick workers squeeze or shutter businesses nationwide.

“I think the odds are we’ll need more legislation. First, we don’t know the extent of the crisis in terms of the magnitude, so that could rise. But there are going to be problems that we don’t realize now that we’re going to have to grapple with,” Senate Democratic Leader Charles Schumer Chuck SchumerSenate Democrats introduce legislation to probe politicization of pandemic response Schumer interrupted during live briefing by heckler: 'Stop lying to the people' Jacobin editor: Primarying Schumer would force him to fight Trump's SCOTUS nominee MORE (N.Y.) said.

“So I think the odds are high there will be a Covid-4,” he added, referring to the anticipated next bill.

The need for additional action from Congress was highlighted by a report Thursday that more than 3 million Americans applied for their first week of unemployment in the week ending March 21, a tremendous spike from recent numbers well under 300,000.

United Airlines CEO Oscar Munoz warned Friday that the company will likely have to lay off workers in the fall because the stimulus package was not big enough.

“Being honest, fair and upfront with you: If the recovery is as slow as we fear, it means our airline and workforce will have to be smaller than it is today,” he said.

The stimulus package includes language in its air carrier worker support subtitle that prohibits airlines from furloughing workers or cutting benefits before Sept. 30, but Munoz warned Friday the slowdown in travel may last into next year.

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Senate Republican Policy Committee Chairman Roy Blunt Roy Dean BluntSocial media platforms put muscle into National Voter Registration Day Senate GOP faces pivotal moment on pick for Supreme Court This week: Supreme Court fight over Ginsburg's seat upends Congress's agenda MORE (Mo.) said he expects another relief bill soon.

“The minute we’re done with phase three, we’ll start talking about phase four because all of us know that phase three can’t have included everything that needs to be included,” he said.

Speaker Nancy Pelosi Nancy PelosiPelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare House lawmakers reach deal to avert shutdown Centrist Democrats 'strongly considering' discharge petition on GOP PPP bill MORE (D-Calif.) also says another stimulus package is needed and on Wednesday vowed that House Democrats would seek to send out another round of direct rebates to low- and middle-income Americans.

"We had bigger direct payments in our bill, and we think we'll get more direct payments in another bill," she said in an interview with CNN.

The package Trump signed into law Friday will send $1,200 rebate checks to American adults earning up to $75,000, with the amounts phasing out above that threshold.

Democrats plan to seek more money for the Supplemental Nutrition Assistance Program and employer-provided pensions facing cash shortfalls. The new relief law provides money for both but not as much as Democrats sought.

Pelosi said she plans to push for pension protection language in the next bill, and indicated Republicans have signaled possible support.

"Pension protections — we had a protection in the legislation. It was supported by everyone. The president of the United States supported it, but McConnell said he would save it for the bill. So that's why I'm mentioning it, for the next bill," Pelosi said on the floor, referring to Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellPelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Senate GOP aims to confirm Trump court pick by Oct. 29: report Trump argues full Supreme Court needed to settle potential election disputes MORE (R-Ky.).

Democrats may also push for emissions restrictions on airlines in return for taxpayer assistance, a request they made and was blocked in the last round of talks.

New York Gov. Andrew Cuomo on Thursday blasted the relief package for falling far short of what his state, the nation’s epicenter of coronavirus infections, will need to recover.

He complained “the congressional action in my opinion simply failed to address the governmental need.”

On Wednesday, Cuomo pointed out the new law will provide only $3.8 billion to New York’s state government while it is facing a revenue shortfall of $15 billion.

Asked about that criticism, New York Sen. Kirsten Gillibrand Kirsten GillibrandSunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election Suburban moms are going to decide the 2020 election Jon Stewart urges Congress to help veterans exposed to burn pits MORE (D) indicated more federal relief is on the way.

“This bill was never intended to be the ultimate effort to make a state whole. This bill was always intended to be triage, to get the most immediate funds to the most urgent places as quickly as possible,” Gillibrand said.

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“That’s why it’s focused on employees, unemployment insurance and money for furloughed workers, as well as a huge amount of money for hospitals because they’re in desperate steps,” she added. “This is a first step. We expect we will be supporting states and local governments and businesses further.”

Business groups say the $2 trillion relief bill will still leave many employers facing significant expenses without adequate revenue coming in because of government restrictions.

“We do need additional help,” said Matthew Haller, senior vice president of government affairs at the International Franchise Association (IFA), which represents corporate brands and small business owners who run their franchises.

Haller said the small-business component of the relief bill allows employers to take out loans up to two-and-a-half times payroll costs but that they will need more capital to cover costs.

“Two-and-half times a franchisee or any other business owner’s average monthly payroll is only going to be about 30 percent of any business owner’s actual cost, so that’s a real limitation in terms of the overall loan size that a franchisee is going be able to take.”

The IFA is pushing for legislation to allow small businesses to take out loans equal to four times total operating expenses.

The American Federation of State, County and Municipal Employees (AFSCME) says the $2 trillion relief legislation is a “good down payment,” but that state and local governments will require more work.

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“More intervention will undoubtedly be required to get our economy moving again — look no further than the fact that a staggering nearly 3.3 million people filed for jobless benefits last week,” said AFSCME President Lee Saunders.

The American Hospital Association also said Congress will need to pass another relief bill.

“While this legislation is an important first step forward, more will need to be done to deal with the unprecedented challenge of this virus,” said group President Rick Pollack.

“We will continue to work with Congress to make sure providers on the front lines — hospitals, physicians and nurses — remain prioritized for future federal assistance as the COVID-19 pandemic spreads,” he said.

There was debate in the Republican conference before passage of the $2 trillion relief bill whether the Senate should even go into recess or stay in Washington to begin working on another round of legislation immediately.

While lawmakers aren’t scheduled to come back until April, McConnell said that could quickly change depending on the conditions across the country.

“The Senate is going to stay nimble,” he said. “If circumstances require the Senate to return for a vote sooner than April 20, we will provide at least 24 hours notice.”

Some lawmakers wonder if Congress should even be leaving town at all.

“There’s some discussions about what would be appropriate because things seem to be changing every day, whether we need to be here monitoring the situation and taking action and communicating to the public about it,” said Sen. John Cornyn John CornynThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight Senate GOP faces pivotal moment on pick for Supreme Court MORE (R-Texas).