Democratic leaders and top Trump administration officials cited real progress on coronavirus aid talks Tuesday, though both sides said there are significant unresolved issues.

In the first indication of a timeline from either side, Treasury Secretary Steven Mnuchin said negotiators hope to reach an agreement by the end of this week so both chambers of Congress could vote on a package next week.

“We’re going to work around the clock for the next few days to see if we can bridge the issues. Some issues we’ve been able to agree on. Some significant issues are still open,” Mnuchin said.

Among the offers Republicans made was a moratorium on rental evictions through the end of the calendar year, Mnuchin said.

White House Chief of Staff Mark Meadows, who has been critical of Democrats thus far in talks, characterized Tuesday’s hour-and-a-half meeting as “productive” and “a step in the right direction.”

He added, however, “I would characterize concessions made by Secretary Mnuchin and the administration as being far more substantial than the concessions that have been made by the Democrat negotiators.”

Democratic leaders, who have been equally critical of their GOP counterparts, were also cautiously optimistic that a deal could be reached.

“They made some concessions, which we appreciated. We made some concessions, which they appreciated. We’re still far away on a lot of the important issues but we’re continuing to go at it,” Senate Minority Leader Charles E. Schumer said. “In my view, the fundamental disagreement is the scope and depth of the problem and its solution.”

Speaker Nancy Pelosi added that “in some cases we’re inching along and in others we’re making more progress, but it takes time.”

Speaking to “PBS NewsHour” separately on Tuesday, Pelosi indicated there remains a stark divide on unemployment insurance.

On the now-lapsed $600 added weekly benefit originally enacted in March, Pelosi said there was “no in-between” amount Democrats would accept. Republicans earlier pitched a $200 weekly benefit until states can ramp up their systems to tailor wage replacement to individual circumstances.

Pelosi said Democrats would welcome extending the evictions moratorium, which applies to about 12 million renters living in federally backed housing. But she also suggested Democrats would push for money to help tenants actually pay their rent, such as the $100 billion assistance fund they included in the nearly $3.5 trillion House-passed relief package.

“Families are in fear of eviction and [Republicans] say, ‘Well we’ll extend the moratorium, but we won’t put any money to help with that rent,'” Pelosi said.

‘Problems with certain parts’

Senate Majority Leader Mitch McConnell, who hasn’t been involved directly in the talks, said earlier Tuesday he’d support whatever agreement the Trump administration and congressional Democrats reach on a coronavirus relief package, even if he has “some problems with certain parts of it.”

The Kentucky Republican, who is up for reelection in November, said his definition of success in the negotiations would be a package “that will actually make a difference” including liability protections for businesses, doctors and schools; money for testing, vaccines and other health care needs; more funds for Paycheck Protection Program loans; and money to help schools reopen this fall.

If the final bill renews the $600 weekly federal boost for unemployment benefits, McConnell said it’s likely many Republicans vote against the proposal.

“I think I’m pretty safe to say that there are plenty of Republicans in the Senate who may not vote for a package if that’s where it ends up,” McConnell said following a closed-door lunch with Senate Republicans, Mnuchin and Meadows.

Mnuchin, Meadows, Pelosi, Schumer and key staff plan to continue meeting daily until they reach a deal.

Both White House negotiators said before the afternoon meeting if Democrats continue to object to their offers they’ll urge Trump to provide some relief through executive action. Following the meeting, Meadows said they’d hope to avoid that path.

“I said as long as there’s progress we’re hopeful that negotiation will provide fruit. I didn’t say we would hold off,” Meadows said.

Sen. Roy Blunt, R-Mo., believes the two sides are getting close to agreement on some of the big areas that are directly related to COVID-19, including funding for vaccine development and distribution, education funding, child care and testing.

“On the areas … that come first to mind when you deal with most of this, we’re pretty close. But not on the areas that don’t relate to COVID,” Blunt said. “We’re not close on their views of helping the state and local governments, but that’s the kind of thing that I think there’s some negotiating space on.”

House Democrats included more than $900 billion in direct aid to states and localities in their bill that passed in May; Senate Republicans didn’t include any additional funds, arguing only a portion of the initial $150 billion appropriated in late March has been spent.

Between rental assistance, unemployment insurance and direct aid to states and localities, those provisions make up about 40 percent of the total price tag of House Democrats’ May aid package.

Mnuchin said Tuesday that Republicans won’t get near the Democrats’ preferred topline. “Let me be clear: We’re not going anything close to $3.4 trillion. So that’s just ridiculous,” Mnuchin said.  

Bad optics

If the impasse continues into next week, several senators have called for that chamber to stay in session instead of leaving Washington for the August recess.

“How do you think it looks for us to be back home when this is unresolved? This is the most important thing we need to be doing,” said Texas GOP Sen. John Cornyn.

Sen. Kevin Cramer, R-N.D., didn’t see remaining in Washington next week as making much of a difference. “I don’t know that we’d get much done other than be here and pound on each other,” he said.

The House is not in session this week and is not planning to return until there is a bipartisan deal for lawmakers to vote on.

Florida GOP Sen. Marco Rubio told reporters earlier Tuesday he’s frustrated talks haven’t moved beyond what he characterized as Democrats trying to demonstrate their firmer negotiating hand.

“I predict that as long as the Democrats believe they can win a [public relations] war on inaction and have it blamed on Republicans, they’re not going to be willing to move,” he said.

Rubio expects GOP senators will go to the floor later this week to request unanimous consent to pass various proposals to show the party is trying to do something, though he would prefer the chamber vote on a bill that can actually pass.

Cramer said he expects Republicans to continue seeking consent for various coronavirus-related provisions to try to force Democrats to speed up negotiations.

“I think there’s a sense that going on offense late last week is helping, in forcing Democrats to object to unanimous consent bills to extend unemployment insurance,” he said. “And you know you wonder how long you do that.”

Jessica Wehrman contributed to this report.