(CNN) The battlelines on Capitol Hill over the next round of emergency funding are hardening amid dire warnings that a popular small business relief program could soon run out of money without the quick intervention of Washington.

The two sides remain far apart and will need to quickly resolve their differences in order to ensure the nation's small businesses can continue to have access to the forgivable loans that were enacted as part of the $2.2 trillion stimulus law , the largest rescue package in American history.

And even if congressional leaders cut a deal, they'll need cooperation from the full membership of both houses to quickly pass the legislation out of both chambers -- since lawmakers are away from Washington. If any lawmaker objects to a deal, members will be forced to return to Washington to cast votes in-person, something that could further delay relief to Americans.

Democrats say a host of pressing matters must be addressed while increasing money to the small business loan program. Republicans say those other matters should wait until the stimulus money has first been spent, arguing the small business program is in the most dire need of cash and must be addressed first.

"Conversations are likely to extend most of the week," said one source involved in the talks.

Democratic leaders on Monday reiterated their demands that additional money for the program -- initially funded at $350 billion -- be tied to more funds for cash-strapped state and local governments, hospitals and food stamp programs. Plus, they said that the small business program should be modified to ensure that loans are properly distributed to under-served communities.

And they added a new demand: More money to establish a national program to test for the novel coronavirus and provide personal protective equipment to front-line health care workers.

"Finally, we all desire an end to the shutdown orders so we can get Americans back to work and back to normal," Senate Minority Leader Chuck Schumer and House Speaker Nancy Pelosi said in a statement. "However, there is still not enough testing available to realistically allow that to happen. We Democrats demand adequate funding for the production and distribution of national rapid testing and personal protective equipment -- it cannot wait."

The comments came after Senate Majority Leader Mitch McConnell and House Minority Leader Kevin McCarthy issued a Saturday statement, calling Democrats' demands "reckless" and for immediate passage of a clean $250-billion increase of the small business program.

"This will not be Congress' last word on Covid-19, but this crucial program needs funding now," the two GOP leaders said.

In addition to the push by congressional Democrats, the Trump administration is also facing pressure from some Republican governors to act quickly to disperse more funding to the states.

Maryland Gov. Larry Hogan, a Republican and the chair of the National Governors Association, said in a statement on Monday that he made the case to Vice President Mike Pence and the White House during a teleconference for an immediate infusion of $500 billion for states.

"The nation's governors are urging Congress to act immediately and appropriate $500 billion specifically for the states and territories," Hogan said in his statement, adding, "We have asked the administration to weigh in so that we can break this logjam in the Senate and get this done for the American people."

That figure is even higher than what congressional Democrats have asked for in an interim aid measure. Pelosi and Schumer have proposed $150 billion in funding for state and local governments to be tied to the small business measure, while Republicans have argued that should be addressed in a subsequent legislative package.

Pelosi gave a readout of the Democratic demands and called for a negotiation with the administration and Republicans during a House Democratic conference call on Monday afternoon.

"We've said to them: let's negotiate. We all care about small businesses and want them to succeed," Pelosi said, according to a Democrat on the call. "Hopefully, we can come to some terms if they will negotiate."

Schumer said Friday that Treasury Secretary Steven Mnuchin had agreed to pursue bipartisan talks to resolve the differences.

As the impasse continues, both chambers of Congress are in recess with lawmakers working mainly from their home states and congressional districts.

The Senate is currently scheduled to come back next week, but senators and aides say there's a good chance this could change and they expect official announcements later this week.

One source familiar with ongoing scheduling conversations told CNN that there are active conversations in the Senate about whether it is even feasible to come back and work at the Capitol safely.

The House won't come back to session unless members need to vote on legislation, according to leadership aides, and they'll be given 24 hours notice if they have to return to the Capitol.

On Monday, House Majority Leader Steny Hoyer's office circulated a notice to members saying that the House is not expected to come back into full session prior to Monday, May 4, "absent an emergency."

The notice further stated that "if the House is required to take action on critical legislation related to the coronavirus response or other legislative priorities, members will be given sufficient notice to return to Washington, DC."

That means that both chambers are likely to be on standby as the pandemic continues and will return to session as needed.

This story has been updated with additional developments Monday.