(CNN) Senate Minority Leader Chuck Schumer said Tuesday that by pressing for liability protections for businesses and health care professionals in the next coronavirus bill Senate Majority Leader Mitch McConnell is just "putting barriers in the way of giving state and local governments desperate money they need."

Schumer said on a conference call with reporters that while he has not seen McConnell's exact proposal, he has serious concerns.

"I haven't seen the details of what he said, but is he saying that if an owner tells a worker they have to work next to somebody who might have coronavirus without a mask or (personal protective equipment), that that owner wouldn't be liable? That makes no sense," Schumer said.

McConnell said Monday that liability protections for business owners, employers health care workers must be included in the next coronavirus legislative package , shielding them from lawsuits as states across the country reopen.

"The whole country will be afraid to go back to work ... if businesses are afraid they're going to be sued constantly," McConnell said in an interview with Fox News Radio on Monday

McConnell said these protections are his "red line" in negotiations for the upcoming coronavirus legislative package.

"The next time we pass one of these relief bills, and we probably will, we will be more directly involved with everybody back here, able to discuss things more easily than remotely," he said, adding, this kind of liability protection "is the one thing that will be part of any new bill."

Schumer's comments come a week after McConnell said he was not sure he wanted to provide any relief to state and local governments, which has been a key priority for Democrats and some Republicans.

But McConnell signaled Monday there would likely be funds approved for state and local relief in the next package.

"There probably will be another state and local funding bill," McConnell said. "But we need to make sure that we achieve something that will go beyond simply sending out money."

Responding to Trump's immigration order

While the order falls short of an outright ban on legal immigration to the US, as Trump initially suggested, it stands to affect thousands of people overseas seeking to come to the country. The Migration Policy Institute, a nonpartisan think tank, estimates that the order would block around 26,000 green cards monthly or 52,000 over the 60-day period it's in effect. The pandemic had already largely cut off immigration to the US: countries have put border restrictions in place, visa services have been suspended and refugee admissions are on pause, among other changes.

Schumer was joined Tuesday on the conference call with Minority Whip Dick Durbin of Illinois and Democratic Sen. Bob Menendez of New Jersey. Schumer said he believes the coronavirus pandemic is "showing America how much we need these folks to help us fight the crisis" and "I think that should help us win new support as we push for this in Covid-4," a reference to the forthcoming legislative package under consideration, which would be the fourth major aid package Congress would pass in response to the coronavirus outbreak.

Schumer said they "want to shine a spotlight on the immigrants who are sustaining our health care system and other essential industries," pointing to how one third of New York's health care workers are immigrants.

The Democratic senators are also urging the administration to extend work authorizations as soon as possible.

"We have to respect their work by protecting them from deportation," Menendez said.

Schumer said it's "despicable" that the Trump administration continues to use "immigrants as scapegoats," and called it "especially disgusting for them to do it now ... at a time when immigrants, including DACA and TPS recipients, are risking their lives by helping feed our nation and keep our hospitals running."

Trump's order doesn't apply to spouses and minor children of US citizens; health care professionals; any member of the US Armed Forces and their spouses and children; and anyone entering for law enforcement or national security reasons.