Gov. Phil Murphy said Monday that New Jersey could be headed toward an "Armageddon" scenario, with an inability to fund public schools and police, if it doesn't receive more federal assistance due to the coronavirus pandemic.

Murphy, a Democrat, said on CNBC's "Squawk Box" that New Jersey's revenues "have fallen off a table" due to the coronavirus.

"Our costs are going up serving folks who have lost their jobs, small businesses that have been crushed, folks who are in the health-care system, et cetera," he said.

New Jersey officials have previously signaled that the state could begin to experience a cash crunch in four to six weeks. Asked by CNBC's Becky Quick whether that could mean an inability to pay teachers and police officers, for example, Murphy said, "that's exactly what I'm talking about."

He said he hoped the federal government would ultimately approve more financial assistance to state and local governments, many of which are facing economic strain due to the pandemic, but "that's the sort of Armageddon that we're looking at. I don't say that with any amount of joy."

Murphy highlighted a bipartisan effort from Democratic Sen. Bob Menendez of New Jersey and Republican Sen. Bill Cassidy of Louisiana to establish a $500 billion assistance fund for state and local governments.

The proposal builds off the $150 billion in direct help that was included in the $2 trillion CARES Act. Menendez and Cassidy are proposing more flexibility for how states and local governments can use the funding.

"That's exactly what the doctor ordered," said Murphy, who has been critical of how states can spend money from the CARES Act.

Treasury Department guidance, among other things, says that states can only use CARES Act funding toward "necessary expenditures incurred" due to the Covid-19 outbreak.

"For instance, your entire education system has been transformed because of Covid-19. Your entire public safety reality has been transformed," Murphy said. "We believe those are eligible costs that need to be addressed."

The Treasury Department did not immediately respond to CNBC's request for comment on Murphy's remarks.

Murphy also criticized Senate Majority Leader Mitch McConnell, R-Ky., who last week signaled support for letting states declare bankruptcy instead of receiving federal funds to cover budget shortfalls.

"The alternative is not bankruptcy," Murphy said. "The alternative is we will gut the living daylights out of the very services that our folks now are desperately relying upon in what is the biggest health-care crisis in the history of our country."

McConnell's office said it had no immediate comment.