"The states that seem to have the problem happen to be Democrat," Trump added.

Later Thursday, President Donald Trump said that it was "interesting that the states that are in trouble do happen to be blue."

Cuomo said that it was "vicious" for McConnell to describe proposals to federally fund the states devastated by the virus as a "blue-state bailout."

"I would certainly be in favor of allowing states to use the bankruptcy route," McConnell said. "It saves some cities, and there's no good reason for it not to be available."

On Wednesday, McConnell, of Kentucky, told radio host Hugh Hewitt that he supports allowing states to declare bankruptcy rather than getting federal money to cover budget shortfalls as tax revenue dives.

"You will see a collapse of this national economy" if states such as New York and California declare bankruptcy, Cuomo said. "So just don't."

"This is one of the really dumb ideas of all time," Cuomo, a Democrat, said during a press conference in Albany.

New York Gov. Andrew Cuomo tore into Sen. Mitch McConnell on Thursday over the Senate Republican leader's support for letting states declare bankruptcy as they grapple with the coronavirus pandemic .

McConnell said of state leaders: "My guess is, their first choice would be for the federal government to borrow money from future generations to send it down to them now so they don't have to do that. That's not something I'm going to be in favor of."

Cuomo, whose state has been hit harder by Covid-19 than anywhere else in the U.S., strongly disagreed.

"The entire nation is dependent on what the governors do to reopen," Cuomo said at the press conference. "But then you're not going to fund the state government? You think I'm going to do it alone? How do you think this is going to work?"

"You want to see that market fall through the cellar? Let New York declare bankruptcy," Cuomo added.

Cuomo has previously criticized Congress and the federal government for not providing nearly enough funding to help his state offset the massive costs inflicted by the coronavirus. Before the massive $2 trillion economic relief package was signed into law by President Donald Trump in late March, Cuomo said it would be "terrible" for the Empire State.

The latest coronavirus relief bill, which is expected to pass the Democratic-led House later Thursday, does not provide funding for state and local governments. Congress is expected to work on at least one additional relief package in the future.

"I would've insisted that state and local funding is in this current bill," Cuomo said at the press conference, "because I don't believe they want to fund state and local governments. And not to fund state and local governments is incredibly short sighted."

"They want to fund small business, fund the airlines, I understand that, but state and local government funds police, and fire, and teachers and schools," Cuomo said.

"How do you not fund police and fire and teachers and schools in the midst of this crisis?" he said. "When you don't fund the state then the state can't fund those services."

The governor paraphrased McConnell's argument as: "Don't help New York state because it is a Democratic state."

"How ugly a thought," Cuomo said. "I mean, just think of what he's saying: People died, 15,000 people died in New York, but they were predominantly Democrats, so why should we help them?"

Maryland Gov. Larry Hogan, a Republican, told Politico on Thursday that the bailout language, which came from McConnell's office, was "complete nonsense."

"These are well-run states. There are just as many Republicans as Democrats that strongly support this," Hogan said.

Cuomo told reporters that he has not contacted McConnell about the issue of state funding and that he doesn't intend to. A spokesman for McConnell did not immediately respond to CNBC's request for comment about the governor's remarks.

Hogan and Cuomo, the chair and vice chair of the National Governors Association, wrote to congressional leaders Tuesday requesting an additional $500 billion state stabilization fund. They said lost revenue during the crisis would force states to make "drastic cuts" to programs and harm the economic recovery from the pandemic.

"While the three supplemental spending laws passed in March have provided relief to the states, none contained direct funding to offset drastic state revenue shortfalls. Unlike the federal government, states cannot borrow to fund continuing operations," the governors wrote.

McConnell's comments have divided some members of his Republican caucus.

Sen. Bill Cassidy, a Republican who represents Louisiana, home of hard-hit New Orleans, plans to introduce a proposal with Democratic Sen. Bob Menendez of New Jersey to provide half a trillion dollars in relief to state and local governments when Congress returns next month.

"We worked hard to make sure state and local governments can maintain essential services necessary for employees and employers to survive. We must protect Americans' financial future," Cassidy said in a statement announcing the plan Sunday.

At the same time, a spokesperson for Sen. Rick Scott, R-Fla., said Thursday that he agrees with McConnell. Earlier this month, he wrote a letter to Treasury Secretary Steven Mnuchin saying that federal aid money "should not be used to backfill lost revenue or plug holes in poorly designed state budgets."