President Donald Trump entered a new week facing continued criticism from governors for his response on providing federal help with testing -- a key component to reopening and avoiding a spike in new cases.

As Trump kept blaming governors for not being more prepared and not doing more, Vice President Mike Pence held a teleconference with them Monday morning.

“Our team presented every governor in the country, states and territories with a memorandum detailing laboratory capacity in all locations of laboratory equipment for diagnostic tests that can perform the coronavirus test,” Pence said.

“We told the governors once again today that by our best estimates, we have enough testing capacity today for every state in America to go to phase one,” Pence said. “If they meet the other criteria of 14 days of reduced cases, and sufficient hospital capacity to prepare for any eventuality that may occur.”

Some states looking to reopen may not necessarily be meeting the White House guidelines, but it's up to governors to makes those decisions, White House coronavirus task force coordinator Dr. Deborah Birx said.

“Each of the governors can decide for themselves whether they have reached specific guidelines in specific areas,” Birx said, using Florida as an a model state.

The president also announced New York Gov. Andrew Cuomo, a Democrat, would visit the Oval Office Tuesday, after the two have gone back and forth on a national stage criticizing each other's response to the pandemic for the past few months.

“I think that the governor’s going to come in to see us tomorrow. He is coming to the Oval Office tomorrow afternoon. Andrew is gonna be coming in with some of his people. So we look forward to that,” Trump said.

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Here are Monday's most significant developments in Washington:

Trump continues to argue states responsible for testing, not federal government

Pence holds video teleconference call with governors to discuss the task force's recommendations for phased reopenings

Trump says New York's governor visiting White House Tuesday

White House and Capitol Hill leaders near deal on replenishing small business loan fund which dried up last week

Here are the latest developments in the government response:

Trump says New York's governor coming to White House Tuesday

President Donald Trump opened his briefing Monday by looking to the “economic resurgence” he says is coming in the wake of his “Opening up America Again” guidelines, as several Republican governors in southern states took the lead Monday and began lifting measures to open businesses amid the ongoing coronavirus pandemic.

“Governors across the country are looking forward to phase one in announcing plans for an economic resurgence,” Trump said. “We continue to be encouraged that many of the areas hardest hit by the virus have turned the corner.”

The president also took the chance to attack some of the nation’s governors, after they had a teleconference call President Mike Pence earlier Monday, for criticizing the federal government’s response on helping states carry out testing.

Trump repeated an argument from his administration that states are not fully taking advantage of labs in their own states, singling out Republican Gov. Larry Hogan who has publicly pushed the president to take more action when it comes to testing.

“Some of the governors like, as an example, the governor from Maryland did not really understand the list. He did not understand too much about what was going on,” Trump said, referring to a list of labs in each state with a testing capacity. “It's pretty simple. But they have tremendous capacity. And we hope to be able to help him out.”

But ABC News obtained an audio recording of that call and Trump totally misrepresented what Hogan said.

On the call, Hogan said he was already “in contact with every one” listed for his state – and that he wasn’t actually even able to use some of them.

He said certain labs were federally run or controlled by the Department of Defense and had been off limits to the state. In response, White House coronavirus response coordinator Deborah Birx told Hogan the task force had spoken with the Defense Department and said “there’s a willingness” on its part to open those labs for the states to use.

The president also announced New York Gov. Andrew Cuomo, a Democrat, would visit the Oval Office Tuesday, after the two have gone back and forth on a national stage criticizing each other's response to the pandemic for the past few months.

“I think that the governor’s going to come in to see us tomorrow. He is coming to the Oval Office tomorrow afternoon. Andrew is gonna be coming in with some of his people. So we look forward to that,” Trump said.

When Pence took the podium, he repeated that it’s up to governors to manage testing in their states.

“Our team presented every governor in the country, states and territories with a memorandum detailing laboratory capacity in all locations of laboratory equipment for diagnostic tests that can perform the coronavirus test,” Pence said.

He also addressed Gov. Hogan’s concern that certain labs that are federally run or controlled by the Department of Defense and had been off limits to the state, saying the White House is working to make those available.

“I was able to assure the governor and every governor on the call that we will make all of those laboratories available across the country to every state as the need for testing capacity continues to scale,” Pence added.

"I am sure the military would offer their facilities to the governor of Maryland or any governor who wanted to utilize both to expand testing," Birx also said.

Pence says all 50 states able to move into 'phase one' of reopening guidelines

Pence said every state in the U.S. has the testing capacity to enter phase one of reopening the country, also implying all 50 states meet the White House’s “gating criteria,” despite a chorus of governors’ continued complaints with the testing supply chain.

“We told the governors once again today that by our best estimates, we have enough testing capacity today for every state in America to go to phase one,” Pence said. “If they meet the other criteria of 14 days of reduced cases, and sufficient hospital capacity to prepare for any eventuality that may occur.”

Some states looking to reopen may not necessarily be meeting the White House guidelines, but it's up to governors to makes those decisions, said a data-driven Dr. Birx.

“Each of the governors can decide for themselves whether they have reached specific guidelines in specific areas,” Birx acknowledged, before using Florida as an a model example state.

“I will tell you that the Florida department of health website is extraordinary,” Birx said. “When you inform the public and give them the information that they need, then they can make decisions along with the local government and governors.”

Officials in Jacksonville, Florida, opened beaches to a restless and crowded public on Friday, and Texas opened state parks Monday with more restrictions scheduled to be lifted as the week progresses, including allowing some elective surgeries to continue Wednesday.

Gov. Henry McMaster of South Carolina also allowed some retail shops to open Monday with social distancing in place, and Gov. Brian Kemp of Georgia announced restaurants gyms, hair salons, and bowling alleys, among other businesses, may begin reopening statewide Friday. And in Tennessee, the "vast majority" of businesses can reopen on May 1, GOP Gov. Bill Lee said.

After Adm. Brett Giroir stressed the importance of testing, saying that the federal government would continue to ramp up its system as states look move beyond phase one of reopening, the president interjected that the U.S. was already doing “the maximum" -- even though some people say that that much testing isn't needed, he claimed.

“And by the way, not everybody agrees that we have to do that much testing. We are going maximum. You understand, there are some people who don't want to do that much testing, but we are going maximum. We’re going to the outer limits,” Trump said.

Asked why Gov. Hogan secured 500,000 COVID-19 tests from South Korea, if there are enough tests for every state to enter phase one, Pence said he “wouldn't begrudge him or his health officials for ordering tests,” while insisting that the U.S. has adequate testing capacity.

President Trump, however, wasn’t as understanding, and pointing to a map of labs with access to testing in the Maryland area created by the White House, suggested Hogan should've educated himself and saved his money.

“Take a look at that map. The governor of Maryland could've called Mike Pence and could've saved a lot of money. Look at all those different places,” Trump said. “Could have saved a lot of money, but that's okay. I don't think he needed to go to South Korea. I think he needed to get a get a little knowledge. That would've been helpful.”

Late Monday, Hogan responded to the president on Twitter.

"I’m grateful to President Trump for sending us a list of federal labs and generously offering Maryland use of them for #COVID19 testing. Accessing these federal labs will be critical for utilizing the 500,000 tests we have acquired from South Korea," he wrote,

From earlier today:

Governors tell Pence they're having trouble keeping people at home, getting testing gear

Democratic governors of Michigan and North Carolina, facing protests against their stay-at-home orders amid the coronavirus pandemic on Monday, asked the White House for help keeping people home, after President Trump had voiced support for the demonstrators.

While Vice President Mike Pence agreed to "make a point" to reiterate social distancing when asked, even GOP governors like Greg Abbott of Texas complained to Pence that states are still having trouble getting access to the medical gear needed to collect samples for COVID-19 tests.

The comments were made on a videoconference call between Pence and governors focused on testing, according to an audio recording obtained by ABC News.

-- ABC News' Katherine Faulders and Ben Gittleson

Anti-quarantine protests planned in parts of country as Facebook takes action to remove events which violate local laws

A Facebook spokesperson says that the company has taken action to remove anti-quarantine events promoted on the website in California, Nebraska and New Jersey after consultation with state governments who said the events violate their respective state stay-at-home orders, ABC News' Alexander Mallin reports.

"Unless government prohibits the event during this time, we allow it to be organized on Facebook. For this same reason, events that defy government's guidance on social distancing aren't allowed on Facebook," a company spokesperson said in a statement.

The Washington Post first reported that a group of three far-right, pro-gun organizers is behind some of the largest Facebook groups calling for anti-quarantine protests around the country.

The Facebook groups they manage have roughly 200,000 members combined and have targeted protests in states like Wisconsin, Ohio, Pennsylvania and New York.

They've continued to expand quickly, days after the president endorsed protests in Michigan, Minnesota and Virginia on Twitter by suggesting citizens "liberate" their states.

As protests are planned for Monday in Harrisburg, Pennsylvania, among other places, to call on governors to reopen economies, Washington Democratic Gov. Jay Inslee said the president's messaging was basically encouraging illegal activity on ABC's "This Week" Sunday.

"To have an American president to encourage people violate the law, I can't remember any time in my time in America we have seen such a thing. It's dangerous, because it could inspire people to ignore things that could save their lives," he told ABC Chief Anchor George Stephanopoulos.

"And it's doubly frustrating to us governors," he added. "The president is asking people 'please ignore Dr. Fauci, Dr. Birx, please ignore my own guidelines I set forth.'"

Treasury official says paper stimulus checks with Trump's name on them have started being sent out

A senior Treasury Department official confirms to ABC News that the economic impact paper checks have already started going out and are in the mail -- walking back Treasury Secretary Steve Mnuchin’s comments Sunday at the White House that physical checks would start going out "next week."

The Trump administration faced criticism for a reported delay in issuing physical checks after the president's name was added to them in what some call an "unprecedented move."

The U.S. Secret Service, working together with the Treasury Department, released an image of what the economic relief paper checks will look like Monday morning in an effort to help Americans and banking institutions avoid scams around counterfeits.

Secretary Mnuchin said Sunday on CNN that checks hadn't been issued to give people more time to sign up for direct deposits -- though the Treasury is now saying the checks are on the way.

Mnuchin also said that putting the president's name on the paper checks going out this week was his idea -- and that he still doesn't have an exact number on ho many paper checks are going out at this time.

"We did put the president's name on the check. That was my idea. He is the president, andI think it's a terrific symbol to the American public."

-- ABC News' Matthew Vann

ABC News Chief White House Correspondent Jonathan Karl asked the president about this last week at a White House Task Force briefing to which the president said he didn't know too much about it.

White House and congressional leaders nearing deal to refund small business loan fund

The Trump administration and congressional leaders are nearing a deal on a roughly $400 billion fund that could pass the Senate as soon as Monday.

The interim funding is to replenish a small business loan program that ran out of money last week, and would also add funding for hospitals and testing, which Democrats pushed for and faced criticism for stalling negotiations with the terms.

Treasury Secretary Mnuchin said on CNN that he hoped to see the agreement pass both houses of Congress early this week. Senate Minority Leader Chuck Schumer also expressed optimism Sunday about getting a deal done "tonight or tomorrow morning."

Fauci warns reopening country too soon could 'backfire'

Dr. Anthony Fauci, the government's top expert on the infectious diseases, warned Monday that lifting social distancing restrictions too soon could "backfire" and lead to a "big spike" in cases, when asked what's his message to protesters chanting "Fire Fauci" as some people push for a reopening.

"Unless we get the virus under control, the real recovery economically is not going to happen," Fauci told ABC Chief Anchor George Stephanopoulos in an interview on ABC's "Good Morning America."

"If you jump the gun and go into a situation where you have a big spike, you're going to set yourself back," he explained. "That's the problem."

Fauci acknowledged the country is "certainly going to need more" testing than the 1.5 to 2 million COVID-19 tests being conducted now per week but expressed optimism the system is improving.

"We need to get up to at least maybe two times that, three times that," he said. "But we will as we go into the coming weeks."