(CNN) The United States' coronavirus death toll topped 40,000 on Sunday afternoon, according to data from Johns Hopkins University .

The 40,461 deaths are among more than 755,533 coronavirus cases , the university's Covid-19 tracker says.

The grim milestone was reached as Harvard researchers warned that if the country wants the economy to open back up -- and stay that way -- testing must go up to at least 500,000 people per day.

Testing nationwide is currently at 150,000 per day, they said, adding that "If we can't be doing at least 500,000 tests a day by May 1, it is hard to see any way we can remain open."

Though some officials have warned against it, several states are looking to reopen as soon as possible. Protesters showed up in the capitals of Colorado, Washington, Indiana, Maryland, New Hampshire and Texas this weekend to decry their states' stay-at-home orders.

The research on the testing shortfall was done by Dr. Ashish Jha, faculty director of the Harvard Global Health Institute, Dr. Thomas Tsai, researcher at the Harvard T.H. Chan School of Public Health, and Benjamin Jacobson, research assistant at the Harvard Global Health Institute.

The number of positive tests must also be much lower, the researchers said. In the US, 20% of those tested for coronavirus get positive results. The World Health Organization has said that to reopen, that number should be between 3% to 12%.

In a three-part guideline released last week, the White House said states can enter the first phase toward reopening once they see a continued decrease over two weeks.

Governors want testing capacities bolstered

The major determining factors behind governors' decisions to reopen their economies should be testing, experts have long said.

President Donald Trump and Vice President Mike Pence say there is ample testing capacity for states to begin the first phase.

But Gov. Ralph Northam of Virginia called the assertion "delusional" and said his state doesn't even have sufficient swabs to conduct testing.

Ohio Gov. Mike DeWine and Michigan Gov. Gretchen Whitmer told NBC's "Meet the Press" they also have concerns.

DeWine said he could perhaps triple testing capacity overnight if the US Food and Drug Administration would prioritize companies that use different formulae in producing their analysis kits.

Whitmer said she is ready to double or triple capacity but can't get enough swabs and the reagents used to analyze tests.

"I'm glad to see that the White House recommended opening in phases," she said. "We can't just turn back to what life was like before Covid-19. We have to be strategic. We have to be careful. We have to look at different sectors of our economy."

Trump responded to governors' complaints Sunday, saying that "testing is a local thing," and that governors "can't have it both ways," because they wanted to have control over reopening their states but also wanted the federal government to provide testing.

Trump also said Pence will call the nation's governors from FEMA headquarters Monday to discuss testing.

Contamination delayed tests

The US is currently lacking the testing capacity critical to reopening, and the rollout of tests was stalled from the start of the national outbreak.

That delay stemmed from contamination in manufacturing the Centers for Disease Control and Prevention coronavirus test, multiple health officials told CNN.

Part of that contamination came from the CDC not adhering to its own protocols, according to the US Food and Drug Administration. It said the test was made in a CDC laboratory instead of one of its manufacturing facilities, which is not consistent with its protocol.

"Routine quality control measures aim to identify these types of issues. Those measures were not sufficient in this circumstance, and CDC implemented enhanced quality control to address the issue and will be assessing this issue moving forward," CDC spokesman Benjamin Haynes said.

States easing restrictions

Some states are already taking steps to begin reopening, though the changes are gradual and limited mostly to outdoor activities.

In South Carolina, Gov. Henry McMaster is expected to announce Monday that he lifted restrictions on beach access and retail stores, according to a report from The Post and Courier newspaper in Charleston. In Florida, residents flocked to Jacksonville beaches after officials announced a soft opening Friday night allowing for recreational activities for several hours each day.

But Jacksonville Mayor Lenny Curry said the openings do not mean the area is done flattening the curve but provide a responsible way to exercise outdoors.

The soft reopening comes on the same weekend that Gov. Ron DeSantis announced that the Florida Department of Health has released the names of 303 long-term care facilities that have reported Covid-19 cases. Of the 1,627 residents or staff members who have contracted the illness, 162 have died, the department said Saturday.

Texas Gov. Greg Abbott issued an executive order Friday easing some measures next week -- ordering state parks to reopen by Monday but directing residents to wear face coverings, keep a distance and stay in groups of five people or fewer. The state has more than 18,000 reported infections.

Abbott said the process of reopening the state will happen gradually and be guided by medical experts.

In Minnesota, Gov. Tim Walz signed an order allowing many outdoor activities -- including golfing, boating, hunting and biking -- to resume Saturday morning, as long as residents follow social distancing guidelines, avoid crowded spaces and stay close to home.

In New York, where Gov. Andrew Cuomo's staff is working with other states to coordinate a regional reopening when it's appropriate, hospitalizations were down Sunday, as was the three-day average of hospitalizations, the governor said.

New York will launch the most aggressive antibody testing initiative in the nation over the next week, he said. Though the data could suggest New York is past its apex, it is only "halftime" in the state's fight, Cuomo said. Any plan to reopen will be based on testing.

"If the data holds and if this trend holds, we are past the high point, and all indications at this point are that we are on the descent," he said. "Whether or not the descent continues depends on what we do."

Vehicles stack up in Boulder during a car protest against the stay-at-home order issued by Colorado Gov. Jared Polis on Sunday, April 19, 2020.

Protests over orders

Trump mentioned the protests Sunday, saying, "I've seen the people. I've seen interviews of the people. These are great people." He added that they have cabin fever and they want their lives back.

"These people love our country. They want to get back to work," he said.

Sunday, protesters gathered outside the Colorado capitol in downtown Denver as a part of the ReOpen Colorado rally, calling on officials to end statewide Covid-19 health orders and reopen the state.

An organizing group is calling on the governor to shift to a targeted quarantine in which elderly immunocompromised populations will be forced to stay at home, CNN affiliate KGMH reported

Hundreds of protesters gather around the Capitol in Olympia, Washington, on April 19, 2020.

Also Sunday, hundreds of protesters gathered outside the Washington state capitol to protest Gov. Jay Inslee's stay-at-home order, CNN affiliate KOMO reported.

Hundreds gathered in front of the Texas State Capitol in Austin on Saturday for a "You Can't Close America" rally. In New Hampshire, a crowd formed outside the State House, urging Gov. Chris Sununu to lift emergency orders.

In Indianapolis, protesters gathered outside the home of Gov. Eric Holcomb to protest his stay-at-home order, which has been extended until May 1. People in cars paraded through Annapolis, Maryland, honking their horns and holding signs asking Gov. Larry Hogan to lift restrictions.

More are planned for the coming days, including in Wisconsin, Kansas and Missouri.

Ben Dorr, who organized the group Wisconsinites Against Excessive Quarantine, told CNN affiliate WFRV he fears economic destruction.

"Hundreds of thousands of workers are out of work. Hundreds and thousands of small family businesses are being destroyed right now under this quarantine, under this lockdown," Dorr told the news station.

Treasury Secretary Mnuchin told CNN's Jake Tapper on Sunday that he thinks it will be only months, not years, before the US economy recovers from the impact of the coronavirus.