CHICAGO (CBS Chicago/CBS News) — Before criticizing large gatherings in Chicago on Sunday, Gov. JB Pritzker appeared on CBS News’ “Face the Nation” – saying he believes the White House should have stepped in earlier to ensure states have the supplies needed for coronavirus testing.

“Much of what came out of the White House for many weeks was not helpful,” Pritzker said Sunday on the program. “We needed the White House to lead on the Defense Production Act to help us get swabs, to help us get VTM, to help us get reagents. That really hasn’t much happened.”

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Pritzker said the White House has informed his office the state will receive 600,000 swabs, which he said he is “very grateful for.” But he said it is his fellow governors who have “risen to the challenge” to meet the needs of states battling the coronavirus pandemic.

Public health experts say testing will be key to allowing businesses to reopen and Americans to return to work. But governors have for several weeks warned testing is scarce and of shortages of supplies including chemical reagents and swabs.

President Donald Trump has frequently touted the country’s testing and last month, Vice President Mike Pence said there is sufficient testing capacity. The White House also released guidelines last week focused on testing, though they placed much of the burden on the states. To address issues with supplies, Mr. Trump told reporters last month he is preparing to use the Defense Production Act to compel an unnamed company to boost production of swabs.

Pritzker said while the Trump administration was correct regarding testing capacity, in that there are enough machines to run the coronavirus tests, there remains a dearth of supplies.

“The White House is helping, and I appreciate it, but it’s not enough,” he said. “It’s not enough today.”

Pritzker said he and other governors have had to bid for supplies in the private market, leaving them to compete against one another.

“I wish that the White House had stepped up earlier,” he said, adding that the Trump administration can still do so when it comes to securing chemical reagents.

Still, the Illinois governor predicted that by mid-summer, the state will be running “tens of thousands” more tests.

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“We’ve, of course, overcome our challenges more recently and increased testing significantly. We’re now among the top 10 states in America, we’re number two for testing,” he said. “We’ve got to get our contact tracing up and going. And then, as I say, we can reopen the economy as we see our hospitalizations begin to wane.”

At his daily coronavirus briefing Sunday, Pritzker announced nearly 3,000 new cases of coronavirus in Illinois, but also the greatest number of tests in one day so far.

A total of 2,994 new cases of COVID-19 were confirmed in Illinois within the past 24 hours on Sunday, Pritzker said. The total number of confirmed cases statewide now amounts to 61,499.

Pritzker said 97 of the state’s 102 counties now have confirmed cases.

A total of 19,417 new tests were reported in the past 24 hours – the highest number in one day.

Meanwhile Sunday, Pritzker also addressed large parties that had to be broken up by Chicago Police overnight. Asked what has to be done to get people to stop congregating, Pritzker on Sunday noted there were many more parties that Chicago Police knew about and stopped before happened.

“The fact is people need to follow the rules. People will get sick if they don’t follow the rules,” Pritzker said. “We need local government and local police to make sure that people are following the rules.”

Pritzker said on “Face the Nation” that the number of cases is beginning to flatten and said the state is starting to prepare for contact tracing, which, like testing, is also crucial for preventing another outbreak of the coronavirus.

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“We are getting ready for a point where we can begin to reopen the economy,” he said.