WASHINGTON — Negotiators on a huge coronavirus relief bill reported slight progress after talks resumed Monday afternoon in the Capitol, with issues like food for the poor and aid to schools struggling to reopen safely assuming a higher profile in the talks.

Multiple obstacles remain, including an impasse so far on extending a $600-per-week pandemic jobless benefit, funding for the Postal Service, and aid to renters facing eviction. Democratic negotiators spoke of progress at almost the very moment that top Senate Republican Mitch McConnell was slamming them for taking a hard line in the talks.

“We are really getting an understanding of each side’s position. And we’re making some progress on certain issues moving closer together,” said Senate Minority Leader Chuck Schumer, D-N.Y. “There are a lot of issues that are still outstanding. But I think there is a desire to get something done as soon as we can.”

After the meeting, Pelosi told her Democratic colleagues on a call that she’s hopeful a deal could be reached this week, but doesn’t know if it’s possible, according to a Democratic aide who was granted anonymity to describe the private discussion.

House Speaker Nancy Pelosi of California, shown at a news conference with Senate Minority Leader Sen. Chuck Schumer of New York, told her Democratic colleagues on a call that she’s hopeful a deal on coronavirus relief could be reached this week, but doesn’t know if it’s possible. Susan Walsh/Associated Press

Treasury Secretary Steven Mnuchin, a lead negotiator for President Trump, said afterward that “we continue to make a little bit of progress” and that the administration is not insistent on a small-bore approach centered on extending the supplemental unemployment benefit and leaving other items for later. A Republican move to advance a slimmed-down relief package has been a recent point of conflict, with Democrats insisting there must be a comprehensive deal.

“We’re open to a bigger package if we can reach an agreement,” Mnuchin said.

On the Senate floor, McConnell, R-Ky., re-upped his complaint that Democrats are taking too tough a line. McConnell is not a direct participant in the talks but is likely to be an important force in closing out any potential agreement.

“The Speaker of the House and the Democratic Leader are continuing to say ‘our way or the highway’ with a massive wish list for left-wing lobbyists that was slapped together a few weeks ago called a coronavirus bill,” McConnell said.

Speaking to reporters after the two-hour session, Democratic negotiators pressed the case for additional food aid, funding for the Postal Service, and the $600-per-week jobless benefit that lapsed last week. The benefit has helped prop up the economy and family budgets as the coronavirus has wrought havoc.

The White House is seeking opportunities to boost Trump, like providing another round of $1,200 stimulus payments and extending the supplemental jobless benefit and partial eviction ban. Pelosi appears intent on an agreement as well, but she’s made it clear she needs big money for state and local governments, unemployment benefits and food aid.

Treasury Secretary Steven Mnuchin, right, and White House Chief of Staff Mark Meadows, second from right, sit down in the office of Senate Majority Leader Mitch McConnell of Kentucky on Capitol Hill on Monday after meeting with House Speaker Nancy Pelosi and Senate Minority Leader Sen. Chuck Schumer to continue their negotiations on a coronavirus relief package. Susan Walsh/Associated Press

“It was productive, we’re moving down the track. We still have our differences, we are trying to have a clearer understanding of what the needs are, and the needs are that millions of children in our country are food insecure,” Pelosi said. “Millions of people in our country are concerned about being evicted. Tens of millions of people are on unemployment insurance.”

Most members of the Democratic-controlled House have left Washington and won’t return until there is an agreement to vote on, but the Republican-held Senate is trapped in the capital.

“I can’t see how we can go home and tell people we’ve failed, so I think that’s going to be a lot of pressure on everybody to come up with something,” said Sen. John Cornyn, R-Texas. “It really is a matter of will. It’s not a matter of substance at this point. This is just a painful period between people finally deciding OK, we want a deal, and then what that deal will ultimately look like.”

Areas of agreement already include the $1,200 direct payment and changes to the Paycheck Protection Program to permit especially hard-hit businesses to obtain another loan under generous forgiveness terms.

But the terms and structure of the unemployment benefit have remained a sticking point, along with the money for state and local governments. Democrats want almost $1 trillion for localities grappling with pandemic-related revenue losses.

Speaking to reporters Monday evening, Trump made clear the two sides were still far apart on that issue.

“They want to bail out cities and states that have been in trouble for years of bad management,” Trump said. “In all cases Democrat-run cities, and we don’t think that’s fair.”

McConnell is insistent on a liability shield against lawsuits by workers, students, and others against institutions seeking to remain open during the pandemic, including businesses, universities and charities.

On Monday, unions representing professional athletes — including NFL players and Major League Basesball players — weighed in against McConnell’s proposal, saying in a letter to lawmakers, “It makes little sense during these uncertain times to both ask employees to return to work and, at the same time, accept all the risk for doing so.”

On unemployment, Pelosi said she’d consider reducing the $600 benefit for people in states with lower unemployment rates. Republicans want to cut the benefit to encourage beneficiaries to return to work and say it is bad policy since it pays many jobless people more money than they made at their previous jobs.

Another sticking point is that Republicans want to give more school aid to systems that are restarting with in-school learning, even as Dr. Deborah Birx, Trump’s top coronavirus adviser, cautioned that schools in areas with spikes in cases should delay reopening.

Pelosi said Monday’s talks featured extensive discussion on reopening schools. Schumer said the discussion got into the details on the dollar figures involving school aid and food aid.

The House passed a $3.5 trillion measure in May, but Republicans controlling the Senate have demanded a slower approach, saying it was necessary to take a “pause” before passing additional legislation. Since they announced that strategy, however, coronavirus caseloads have spiked and the economy has absorbed an enormous blow.