Speaker Nancy Pelosi has warned that Congress may not pass another round of funding for a key small business payroll relief programme for another week or two, even though the programme is set to run out of money on Thursday.

Ms Pelosi told reporters on Thursday that she hopes an interim relief bill that would include money for the Treasury Department’s paycheck protection programme (PPP) could pass Congress "by the end of the month."

While Republicans are clamouring for Democrats to join them in passing an additional $251bn for the paycheck programme on top of the $350bn Treasury has already doled out to small businesses through banks, Democrats have raised concerns that that money has not been distributed equitably to minority-, women-, tribal-, and veteran-owned businesses that don’t have relationships with large banks.

Ms Pelosi is negotiating for $60bn of the $251bn in the interim relief bill to be earmarked for "community development financial institutions" that provide capital to small businesses in poor and otherwise underserved communities.

Democrats say they will hold fast to their request for $150bn in additional funding for states and local governments, $100bn more for hospitals, and a 15 per cent increase in the maximum benefits for food stamp beneficiaries.

All of that — except the food stamps expansion — would supplement similar measures included in the so-called CARES Act, the federal government’s $2.2trn economic stimulus package from March that was the most expensive bill in US history.

Democratic negotiators have been meeting with Treasury Secretary Steven Mnuchin and his advisers throughout the week to reach a deal on the interim bill before moving onto discussions for a more expansive follow-up “CARES 2” package.

"Negotiate, negotiate, negotiate. That's what we do," Ms Pelosi said on Thursday, continuing her recent penchant over the last few weeks for repeating words in a series of three.

The speaker said Democratic negotiators will meet with Mr Mnuchin again on Thursday afternoon.

“We're hopeful they will come back with something that strikes a balance with what we know we need to do," she said.

Meanwhile, Republicans are framing the prolonged negotiations over more funding for the small business relief programme as Democrats letting an essential government service run dry as social distancing guidelines to fight coronavirus are putting millions of Americans out of work.

"All it simply takes is the Democrats to say yes. I don’t know what more it takes. There are 5 million reasons today. 22 million this month,” said House Minority Leader Kevin McCarthy, alluding to new unemployment claims from the past week and the month of April overall.

“This is not a time to play politics,” Mr McCarthy said as White House officials on Thursday began calling on Democrats to return to Washington to address the paycheck programme and other virus-related matters.

Donald Trump and other White House officials have broadly targeted 1 May to begin re-opening some parts of the economy, but they contend restrictions should be loosened on a state-by-state basis, depending on how affected by the pandemic certain regions are.

“We think that some of the governors will be in really good shape to open up even sooner” than the 1 May target date, Mr Trump said at his daily press briefing on Wednesday.

“Others are going to have to take a longer period of time,” Mr Trump said.

But Democrats and health experts have warned that the US does not have the testing capacity to ensure Americans can go back to working in person safely.

Reopening the economy without proper testing or “contact tracing” — the ability to track and quarantine people who have come into contact with others who have tested positive for Covid-19 — could lead to a resurgence of the coronavirus infection rate, they warn.

Health experts have said the US needs to be testing 500,000 people per day at a minimum.