On the heels of the largest stimulus package passed in U.S. history, lawmakers on Capitol Hill and administration officials are contemplating yet another piece of legislation to provide economic relief amid the coronavirus outbreak.

The latest indication came Monday, when Treasury Secretary Steven Mnuchin said he would be willing to ask Congress for more money for small businesses and those in the private workforce should it be necessary.

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A key piece of the $2.2 trillion relief bill passed last week is $350 billion in funding for small businesses. Businesses with fewer than 500 employees are eligible for up to $10 million in loans, which can be used for payroll and other expenses, like insurance premiums, mortgages, rent or utilities.

“This is a very popular program with Republicans and Democrats, and the president likes it a lot,” Mnuchin told Fox Business’ Stuart Varney Monday. “If we run out of money, and this is a huge success, we will absolutely go back to Congress and ask for more money.”

Congressional Republicans and Democrats also had signaled over the weekend that there could be a fourth coronavirus response bill.

“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 Minority Leader Chuck Schumer, D-N.Y., told The Hill. “So I think the odds are high there will be a COVID-4.”

House Speaker Nancy Pelosi, D-Calif., also expressed the need for further legislation, telling CNN that Democrats “had bigger direct payments in our bill, and we think we’ll get more direct payments in another bill.”

Democrats, in a fourth stimulus package, are reportedly seeking additional funding for the Supplemental Nutrition Assistance Program (SNAP), also known as food stamps, as well as emissions restrictions on airlines — a measure that was blocked from inclusion in the package passed last week.

Pelosi also said that she planned to push for pension protections which did not make it into phase three of the stimulus package. Pelosi said last week that pension protections were supported by President Trump, but that Senate Majority Leader Mitch McConnell, R-Ky., said he would save it for another piece of legislation.

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But House Minority Leader Kevin McCarthy, R-Calif., stressed that phase three of coronavirus legislation – the one approved last week – was “critical,” voicing uncertainty over whether another bill is necessary.

“I’m not sure we need a fourth package,” McCarthy said on Fox News' “Sunday Morning Futures.” “And before we go to start drafting a fourth package, I’d like these three packages just put out…to take care and get this economy moving.”

The 880-page coronavirus stimulus package amounted to the largest economic relief bill in the history of the U.S., with massive amounts of aid slated for individuals, large corporations and small businesses — and its unanimous passage in the Senate came despite concerns on both sides about whether it involved too much spending, or not enough.

Democrats said the package specifically would help replace the salaries of furloughed workers for four months, rather than the three months first proposed. Furloughed workers would get whatever amount a state usually provides for unemployment, plus a $600-per-week add-on.

The package also gives $1,200 per adult and $500 per child directly to the public.

But at the state level, governors have complained that the stimulus package didn’t do enough for them.

“The congressional action in my opinion simply failed to address the governmental need,” New York Gov. Andrew Cuomo said last week. “I’m disappointed, I said I was disappointed. I find it irresponsible, I find it reckless.”

He added that the money New York does receive from the stimulus package was “earmarked only for COVID virus expenses, which means it does absolutely nothing for us in terms of lost revenue.”

It is unclear exactly what could be included in a fourth response package and when provisions might be proposed, as both the House and Senate are on recess.

As of Monday morning, the U.S. reported more than 143,500 positive cases of COVID-19 and more than 2,500 deaths.

Fox Business Network's Megan Henney and The Associated Press contributed to this report.