“They think they have political leverage over the president of the United States and so they’re willing to personally increase the pain for vulnerable families unless they get their way on matters not related to Covid,” McConnell claimed on the Senate floor. “Republicans wanted to agree on the things we could agree to. Democrats said our way or the highway.”

But Schumer rebutted the GOP's claims, saying the White House and top Senate Republicans were the ones who refused to compromise, leading to inaction on critical issues including testing, education funding and additional stimulus payments.

"Rather than compromise, our Republican counterparts said, 'Take a hike,'" Schumer said. "Quite literally they said virtually this in the room: ‘It's going to be our way or no. We're not going to meet you in the middle.'"

Schumer added: "This Republican Party is so tied in a knot it can't agree on anything. It can only spew the same political speech day after day."

Talks between the White House and Democratic leaders collapsed on Friday after two weeks of unsuccessful closed-door negotiations. Trump then issued a series of executive actions on Saturday he said would address the ongoing economic crisis from the coronavirus pandemic. The actions included a memo ordering federal agencies to take steps to reduce evictions, extensions of the suspension of student loan payments and interest and of federal unemployment benefits at a lower rate, and the deferral of payroll taxes.

Democrats lambasted Trump's actions as ineffectual and legally dubious, although they have not filed any legal challenges yet.

"The bottom line is even if [the orders are legal], they're not going to what's needed or come even close," Schumer told Capitol Hill reporters on Monday.

The Senate will remain in session but with no scheduled votes unless there is an agreement, McConnell and other GOP senators said. The vast majority of senators are out of town with a 24-hour notice to return if a vote is scheduled.

As for House Democrats, House Majority Leader Steny Hoyer (D-Md.) announced on the Monday that there will be no votes until the week of Sept. 14, unless an agreement on more Covid relief is reached.

The impasse over a new coronavirus relief package comes as the United States now has seen 5 million cases and more than 160,000 deaths from the disease. The economy is also showing little sign of improvement. The Labor Department reported Friday that the economy added 1.8 million jobs in July, but job growth also slowed down and the unemployment rate remains at 10.2 percent.

On top of the high unemployment rate, a federal moratorium on evictions and a federal $600 weekly unemployment benefit expired last month, leaving millions of Americans in a state of economic uncertainty.

The White House last week offered a $400 weekly unemployment benefit through mid-December, which Democrats, who are seeking an extension of the full $600 in boosted weekly assistance, rejected. Democrats have also pushed back on any type of short term deal, arguing they don’t want to negotiate in a “piecemeal” fashion.

The biggest sticking point remains the price tag. Democrats are pushing the nearly $3.5 trillion HEROES Act the House passed in May, but the White House and Senate Republicans want to keep the number closer to $1 trillion. Schumer and Pelosi said last week they offered to go down $1 trillion if the White House went up $1 trillion, but White House chief of staff Mark Meadows and Treasury Secretary Steven Mnuchin refused that offer.

Mnuchin said Monday on CNBC that “there is a compromise if the Democrats are willing to be reasonable.”

"If we can get a fair deal, we'll do it this week,” Mnuchin said. “But the president needed to take action. He's not going to sit around. We left the meeting on Friday, Mark Meadows and I, reported back to him that we were nowhere and that's why he moved forward.”

As senior administration official said the White House doesn't see the likelihood of any deal being reached this week, or even in coming weeks. Administration officials noted the financial markets remained solid to begin the week, showing no sign of panic by investors that an agreement hadn't been reached.

However, government funding runs out on Sept. 30. And even if partisan battles block talks on a Covid relief package now, the looming election on Nov. 3 and the funding deadline may force both sides to reconsider their positions. So could a downward shift in economic data, especially with enhanced federal unemployment payments having expired on July 31.

Ben White contributed to this report.