WASHINGTON — A new lending program for small businesses maxed out Thursday morning and stopped accepting claims, but negotiations picked up between Democrats and the Trump administration to address that growing problem as the nation plunged into unemployment levels not seen since the Great Depression.

The Small Business Administration said on its website that the agency “is unable to accept new applications . . . based on available appropriations funding.”

The $350 billion Paycheck Protection Program was a central piece of the massive $2 trillion economic rescue law passed three weeks ago. Republicans and Democrats say more action is needed to build on the law, but they have not been able to agree on what to do. The economy continues to crumble, but lawmakers are scattered all over the country, advancing conflicting proposals and bickering.

The impasse became so heated that President Trump lashed out at House Speaker Nancy Pelosi, D-Calif., on Thursday morning, a day after he threatened to adjourn Congress because of what he characterized as nothing being done. Pelosi dismissed Trump as “a weak person.”

By the end of the day Thursday, Trump said his administration was negotiating with Democrats and that he expected “something’s going to be happening.”

The Paycheck Protection Program was overwhelmed by demand from the moment it launched April 3, and the program has essentially run dry as small businesses around the nation ask for relief. The program is aimed at helping businesses with less than 500 workers and keeping people employed by extending loans that are forgivable if businesses keep workers on payroll.

The SBA reported Thursday morning that more than 1,637,000 loan applications valued at “over $339 billion” had been approved. It is not expected to disclose who the recipients of the taxpayer funds will be; the $2 trillion bailout law did not compel the agency to make this information public.

President Trump speaks about the coronavirus at the White House on April 1. Alex Brandon/Associated Press

The government has not released data showing how much of that cash has been disbursed and given to the small businesses. Anecdotal reports from lenders and small business owners suggest a small portion of it has been released, with many banks overwhelmed with applications. It is also unclear how many firms have secured new loans, though it appears to be a small portion of the 30 million small businesses in the United States.

Last week, Treasury Secretary Steven Mnuchin asked Congress to agree to $250 billion more for the program, but a Republican attempt to approve that increase failed in the Senate as Democrats demanded more money for hospitals, cities and states and food stamp recipients.

There had been scant progress for the past week, but talks started Wednesday with aides to Mnuchin, Pelosi and Senate Minority Leader Chuck Schumer, D-N.Y. They did not yield results in time for action at a brief Senate session Thursday afternoon, as some had hoped. But the negotiations were ongoing, with Trump sounding notes of optimism at his daily coronavirus briefing Thursday evening even while criticizing Democrats’ demands.

“We’re negotiating with Democrats. And they should, frankly, approve it quickly. This is a great thing for our country. It’s a great thing for small business and for the workers,” Trump said. “And we’re having a hard time getting them to approve it. I think it’s going to happen. It should happen really unanimously. But they’re trying to get things and we’re not too happy with what they’re trying to get.”

Democrats have blamed Republicans for the impasse, accusing them of refusing to negotiate over their demands for targeted assistance, such as more relief for hospitals, and for city and state budgets that have been hammered by a drop in revenue. Governors of both parties have been begging Congress to approve $500 billion more in stabilization funds to help them weather the economic catastrophe.

Pelosi told reporters on a conference call Thursday that instead of asking Democrats why they are blocking more small-business money, Republicans should explain why they are standing in the way of increases for health-care facilities and state and local budgets.

Speaker of the House Nancy Pelosi, D-Calif., talks during a news conference Feb. 6 at the Capitol in Washington. President Trump and Pelosi have not spoken in five months at a time when the nation is battling its worst health crisis in a century. J. Scott Applewhite/Associated Press

“I turn the question on them,” Pelosi said. “When we all know we want to help small businesses, why would you turn your back on the hospitals who are delivering the services?”

Republicans have argued that the need for small businesses is more immediate, but Pelosi disputed that. “It’s very, in our view, self-evident that that need for state and local and hospitals is urgent now,” she said. Pelosi said negotiations were ongoing, and also said Democrats wanted to see more data on how the small business program has functioned, but she said talks were continuing.

The need is deepening on all sides, as new figures released Thursday showed that unemployment claims once again surged over the past week, with 5.2 million people filing for unemployment insurance. More than 22 million Americans have filed for unemployment aid since Trump declared a national emergency four weeks ago.

As the day began, Trump criticized Pelosi on Twitter, following that up several hours later with another tweet accusing Democrats of “killing American small businesses” by blocking additional funding for the small-business program.

The PPP is a major component of the Trump administration’s efforts to blunt the economic effects of the coronavirus, which has been especially devastating for small businesses.

It is meant to offer loans for small businesses totaling up to $10 million at very low rates. Borrowers get an interest rate of 1% and can have the loan entirely repaid if they keep paying their employees.

President Trump and Jovita Carranza, administrator of the Small Business Administration, listen as Treasury Secretary Steven Mnuchin speaks about the coronavirus at the White House on April 2. Alex Brandon/Associated Press

Under the PPP, private banks handle the work of accepting applications, evaluating borrowers’ needs, setting the precise terms of the loan and transferring the cash. The SBA and the Treasury Department are responsible for approving lenders and establishing the rules.

The program got off to a rocky start with big U.S. banks, including Citigroup, taking several days to launch and many only accepting applications from their existing customers. But within days, bank officials began to warn that the $349 billion would not last long.

This week, JPMorgan Chase said it has funded $9.3 billion of the loans and was processing 300,000 applications seeking $36 billion. Bank of America says it has received applications seeking more than $40 billion in loans.

The Federal Reserve eased restrictions it had put on Wells Fargo’s growth after the bank said it had received applications worth more than $10 billion in loans over a few days.

The banking industry is calling on Congress to increase the program’s funding. “Additional funding for all lenders is needed now to ensure there are no breaks in service to small businesses seeking assistance as a result of the coronavirus outbreak,” said Richard Hunt, president of the Consumer Bankers Association. In the next round of funding, 25 percent of the $250 billion should be set aside for small community banks to make these loans, according to the Independent Community Bankers Association.

The PPP program reached its funding limit while a separate program, called Economic Injury Disaster Loans, is also running short on funds. The funding shortfall has already caused that program to slash the size of loans it gives to small businesses, SBA officials say.

In a statement Wednesday, Mnuchin and SBA Administrator Jovita Carranza warned that a lapse in appropriations threatens to further disrupt the loan programs.

“By law, the SBA will not be able to issue new loan approvals once the programs experience a lapse in appropriations,” Mnuchin and Carranza wrote. “We urge Congress to appropriate additional funds for the Paycheck Protection Program – a critical and overwhelmingly bipartisan program – at which point we will once again be able to process loan applications, issue loan numbers, and protect millions more paychecks.”

In the statement, Mnuchin and Carranza defended the two loan programs amid criticism from members of Congress and industry groups. They said the SBA has processed more than 14 years’ worth of loans in less than two weeks, and said the program is already “saving millions of jobs and helping America’s small businesses make it through this challenging time.”