Top GOP leaders in Congress said Saturday they would not negotiate with Democrats and instead insisted that lawmakers approve more money for a small-business lending program for firms impacted by the coronavirus pandemic.

Senate Majority Leader Mitch McConnell (R-Ky.) and House Minority Leader Kevin McCarthy (R-Calif.) released a joint statement Saturday morning saying they would not agree to any compromise with Democrats that changed their proposal to add $250 billion to the Paycheck Protection Program, which is being run by the Small Business Administration.

“Republicans reject Democrats’ reckless threat to continue blocking job-saving funding unless we renegotiate unrelated programs which are not in similar peril,” the joint statement said. “This will not be Congress’s last word on COVID-19, but this crucial program needs funding now. American workers cannot be used as political hostages.”

Their statement appeared to deepen a stalemate over Congress’s next steps to address the nation’s economic misery.

The small-business Paycheck Protection Program, initially funded at $350 billion, was part of the $2 trillion rescue bill Congress approved late last month to deal with the economic ravages of the coronavirus.

McConnell and McCarthy claimed in their statement that the program “burned through roughly half of its initial funding in the first week.” They didn’t provide more information about this claim, and it doesn’t appear to track with how the program was designed.

The program incentivizes banks to make loans to small businesses. Those loans are forgivable, meaning they don’t have to be repaid if the companies meet certain metrics such as job retention. But the government funding isn’t supposed to be used for the initial loans, and so the $350 billion in taxpayer money should still largely be intact unless the SBA and Treasury Department advanced the money to banks, which they have not announced they would do. Still, the fact that the White House now considers much of these funds to be “obligated” for future repayments to the banks is adding to their sense of urgency for updating the program.

The White House has said the program proved so popular in its first week that more money was needed for this purpose. It still appears just a fraction of the nation’s 30 million small businesses are participating in the program, and many firms have complained that banks aren’t cooperating enough or providing faster assistance.

Democrats don’t want to sign off on the $250 billion increase without also adding hundreds of billions for hospitals, cities, states and food stamp recipients. They also want to ensure that half of the increase goes through community banks, emergency grants and other programs aimed at underserved communities.

Democrats blocked an attempt by McConnell on Thursday to advance the $250 billion increase, while McConnell blocked an effort by Democrats to block a competing relief bill with money for the small-business program as well as other priorities.

The Paycheck Protection Program has been swamped by overwhelming demand, even as lenders have griped about confusing regulations and small businesses have complained about difficulties accessing the program and actually getting the money. Speaking on Fox Business on Friday, White House economic adviser Larry Kudlow said more than 660,000 loans have been approved for a total of $168 billion, meaning nearly half the money in the program already has been obligated.

He said the money was forecast to run out on April 17.

“Those are enormous numbers,” Kudlow said. “That’s why we would like the Congress to help us with an additional $250 billion.”

President Trump said at the daily briefing of his coronavirus task force Friday that he was open to Democrats’ demands, which include an additional $100 billion commitment for hospitals and health-care systems; $150 billion to help cities and states; and a 15 percent increase in food stamp benefits. But Trump suggested those should come in a later recovery package, perhaps along with a payroll tax cut and an infrastructure bill, two priorities he has been pushing for some time.

“I’m certainly okay with helping the states and helping the hospitals,” Trump said, but he added that the Paycheck Protection Program is getting “swamped.”

Republicans argue that the small-business loan program is the one piece of the $2 trillion Cares Act that is in immediate need of a cash infusion, since other portions of the bill — such as unemployment insurance and aid to hospitals, cities and states — are rolling out more slowly.

The statement from McConnell and McCarthy followed comments from Democratic leaders on Friday about the need for negotiations in response to the administration’s $250 billion request for the small-business loan program.

Senate Minority Leader Charles E. Schumer (D-N.Y.) said he had spoken with Treasury Secretary Steven Mnuchin on interim emergency relief legislation for coronavirus. "There’s no reason why we can’t come to a bipartisan agreement by early next week,” Schumer said.

House Speaker Nancy Pelosi (D-Calif.) also had a conversation with Mnuchin, according to her spokesman, Drew Hammill. Pelosi reiterated the Democrats’ contention that the small-business initiative “must not solidify the disparity in access to capital faced by many small businesses in underserved areas” and that any agreement also should include money for hospitals and state and local governments.

Despite the contention from McConnell and McCarthy that no negotiations were needed, some other Republicans were open to talks that could improve the program.

Sen. Rob Portman (R-Ohio) said in an interview Friday with The Washington Post that while he supported McConnell’s effort to boost funding for the program, he is also seeking tweaks to how it is administered — citing concerns about some businesses, such as in the hospitality and tourism sectors, that already have laid off thousands of employees.

“I don’t think the legislation works as well for those kinds of businesses,” Portman said. “We agree there ought to be an increase in the cap. But also we think we should be looking at more flexibility to handle those kinds of businesses that really were required to let their people go because they were shut down by governmental action.”

Congressional negotiations are complicated by the fact that the House and Senate are both out of session because of health concerns, and although they are scheduled to reconvene in late April it’s uncertain whether they will actually do so. Without lawmakers physically present, the only way to move legislation is through unanimous consent or voice vote during one of the regularly scheduled and brief “pro forma” sessions that occur a couple of times a week in each chamber. That requires bipartisan consensus and gives any individual lawmaker the ability to block legislation from moving by raising an objection.

On Saturday morning, governors across the United States, through the National Governors Association, called upon lawmakers to shore up collapsing state budgets to the tune of $500 billion in the next relief package.

“In the absence of unrestricted fiscal support of at least $500 billion from the federal government, states will have to confront the prospect of significant reductions to critically important services all across this country, hampering public health, the economic recovery, and — in turn — our collective effort to get people back to work," wrote Maryland Gov. Larry Hogan (R), the NGA chair, and New York Gov. Andrew M. Cuomo (D), the vice chair, in a statement.

Mike DeBonis contributed to this report.