A chorus of governors from both parties pushed back hard after U.S. President Donald Trump accused Democrats of playing "a very dangerous political game" by insisting there is a shortage of tests for the coronavirus. The governors countered that the White House must do more to help states do the testing that's needed before they can ease up on stay-at-home orders.

Public health experts say the U.S. needs to dramatically increase its testing infrastructure if it is going to safely roll back restrictions and reopen businesses without risking a major spike in infections.

Almost 805,000 Americans have come down with COVID-19, the respiratory illness caused by the novel coronavirus, and more than 43,000 have died, according to figures compiled by Johns Hopkins University in Baltimore as of 3 p.m. ET on Tuesday.

Supply shortages have stymied U.S. testing for weeks. The needs range from basic supplies like swabs and protective gear to highly specialized laboratory chemicals needed to analyze patient results. Hospitals, laboratories and state health departments report scouring the globe to secure orders, competing against each other and their peers abroad.

The governors' plea for stepped-up co-ordination came Monday when the Trump administration again provided discordant messaging: Trump blasted state leaders on Twitter for being too dependent on the federal government and said later that some governors just didn't understand what they had, while Vice-President Mike Pence assured governors the federal government was working around-the-clock to help them ramp up testing.

If it strikes you as atypical that in the midst of a national emergency, a state is directly airlifting emergency response materials from another country, well, you'd be right. - Illinois Gov. J.B. Pritzker

Pence sought to soften the administration's message amid growing clamour from both parties for a national testing strategy to help secure testing swabs, chemical reagents and other crucial supplies.

"When it comes to testing, we're here to help," Pence told governors during a video conference from the headquarters of the Federal Emergency Management Agency (FEMA). The Associated Press obtained audio of the call.

Pence said the administration sent each state a detailed list Monday of testing capacity. But Maryland Republican Gov. Larry Hogan said much of the unused lab machinery listed for his state was in federal labs the state does not have access to. Pence said the administration has agreed to open up federal labs to help states.

Hogan announced Monday that the state had received 500,000 tests from South Korea — a "game-changing" deal negotiated by his wife, Yumi Hogan, who grew up outside Seoul.

"They want the states to take the lead, and we have to go out and do it ourselves, and so that's exactly what we did," Hogan said.

Trump didn't take that lying down. In his daily briefing, he said some governors have "more capacity than they understand."

"The governor of Maryland could have called Mike Pence, could have saved a lot of money," Trump said. "I don't think he needed to go to South Korea. He needed to get a little knowledge."

Hogan thanked Trump in a subsequent tweet, though some observers detected a bit of shade as he explicitly mentioned the Korean purchase:

I’m grateful to President Trump for sending us a list of federal labs and generously offering Maryland use of them for <a href="https://twitter.com/hashtag/COVID19?src=hash&ref_src=twsrc%5Etfw">#COVID19</a> testing. Accessing these federal labs will be critical for utilizing the 500,000 tests we have acquired from South Korea. —@GovLarryHogan

'General cry' for reagents, swabs

In Ohio, Republican Gov. Mike DeWine said his state is working with another federal agency, the Food and Drug Administration (FDA), to find a source of reagent, the chemical used to analyze test results. "A lot of good things are going on, but we're not there yet," DeWine said.

Democratic Montana Gov. Steve Bullock said his state received 5,000 nasal swabs Monday from FEMA — evidence the federal government is listening. But he added, "It doesn't get us far enough."

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In New York, Democratic Gov. Andrew Cuomo said the states should take the lead on testing, but it's up to the federal government to help sort out supply chain issues facing testing manufacturers.

"What the states will run into is when you talk to those labs ... they buy machines and equipment from national manufacturers," said Cuomo, who is expected to meet with Trump at the White House Tuesday. "And those labs can only run as many tests as the national manufacturers provide them chemicals, reagents and lab kits."

Pennsylvania Democratic Gov. Tom Wolf said, "We need the reagents, we need the test kits and I think that's the sort of general cry from other states."

The White House said the Pentagon is finalizing negotiations with a Maine medical company to ramp up production of nasal swabs under the Defence Production Act. An Ohio manufacturer of cotton swabs has also agreed to convert its facilities to allow for 10 million testing swabs per month.

Shortage of PPE also still an issue

Even as testing supplies are paramount, states are still often also fighting for scarce personal protective equipment.

Illinois Gov. J.B. Pritzker arranged a large shipment of PPE from China in the past week.

"If it strikes you as atypical that in the midst of a national emergency, a state is directly airlifting emergency response materials from another country, well, you'd be right," Pritzker said on Sunday. "But that's the landscape that we're operating in, competing with other states, other countries, and even our own federal government for supplies."

Illinois Gov. J.B. Pritzker has found himself on the receiving end of barbs from President Donald Trump for criticizing what he has characterized as a lack of federal co-ordination. (Tyler LaRiviere/Chicago Sun-Times/The Associated Press)

As the pandemic has spread, Pritzker along with Cuomo has been one of Trump's most frequent targets for criticism among U.S. governors.

Meanwhile, Congress reached a tentative agreement Tuesday on a nearly $500 billion US coronavirus relief bill that would replenish a small business rescue program, provide hospitals with another $75 billion, and implement a nationwide virus testing program to facilitate reopening the economy.

Senate Democratic leader Chuck Schumer announced the agreement Tuesday morning and Trump tweeted his support hours later, saying he'll sign the bill if it passes both chambers.

Republican Senate Majority Leader Mitch McConnell has yet to publicly comment on the emerging deal, keeping his counsel until the Senate opens.

Most of the funding, more than $300 billion, would go to boost a small-business payroll loan program that ran out of money last week. An additional $75 billion would be given to hospitals, and $25 billion would be spent to boost testing for the virus, a key step in building the confidence required to reopen state economies.