House Speaker Nancy Pelosi promises the next coronavirus relief bill will include money for the hard-hit states and local governments.
It comes as lawmakers on the other side of the aisle sound off about the amount of debt these measures are adding to the country.
Senate Majority Leader Mitch McConnell is among some Republicans signaling resistance.
The call for help from governors, however, has been bipartisan.
Democrat Phil Murphy, of New Jersey, on NBC's "Meet the Press," talked about the toll on his state.
"We won't go bankrupt, but we'll gut the living day lights out of educators, first responders, the folks we desperately need," said Gov. Murphy.
Republican Larry Hogan, of Maryland, on CBS' "Face the Nation," said, "We're on the front lines. We can't provide services to the people in our states and help us get out of this economic problem without that assistance."
Treasury Secretary Steven Mnuchin said Sunday that the White House would consider additional support for the state and local governments, and also expressed optimism about an economic bounce back starting in July.
White House economic adviser Kevin Hassett, however, said to expect some shocks on the immediate horizon.
"I think that the next couple of months are going to look terrible. You're going to see numbers that are as bad as anything that we've ever seen," said Hassett.
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