Ahead of Trump’s visit to his state Tuesday, Arizona Gov. Doug Ducey tweeted a graphic illustrating guidance from the Centers for Disease Control and Prevention on applying face coverings with the hashtag "MaskUpAZ." Trump came to Arizona to commemorate the 200th mile of “new border wall” in San Luiz and deliver an address to young Americans at Dream City Church in Phoenix.

Phoenix Mayor Kate Gallego, a Democrat, distanced herself from the event in a statement Monday.

“While I do not believe an event of this magnitude can be held safely, particularly as Arizona sees rising Covid cases, the president has decided to continue with this rally,” Gallego said, adding that church and campaign staff have been informed of the city’s masking policy and that all participants, including Trump, should wear a face covering.

Neither the president nor many of those in the crowd followed the mayor's instructions, however, according to reporters on the scene in Phoenix.

Arizona hit another record high in new cases of Covid-19, the disease caused by the novel coronavirus, on Tuesday, The Arizona Republic reported. Daily hospitalizations also exceeded 2,000 for the first time.

Across the state, at least 80 percent of intensive care unit beds have been occupied since June 14. As of Monday, 1,412 ICU beds — 84 percent — were in use.

Texas, meanwhile, tallied more than 5,000 new cases in a single day for the first time Tuesday. “The coronavirus is serious. It’s spreading,” Texas Gov. Greg Abbott told a local television station, as he urged people to stay inside and wear face masks when venturing out.

Florida Gov. Ron DeSantis acknowledged at a briefing in Orlando on Tuesday that the state has seen “a real explosion in new cases” over the past week among younger residents. Florida officials are cracking down on bars and restaurants that violate occupancy limits and social distancing recommendations, DeSantis said, decrying “packed” establishments that are “like mayhem” and “dance party USA.”

“The message is just stick with the basic program that we’ve advised really from the beginning,” he said. “It’s still important to maintain the appropriate physical distance. It’s very important to exercise good hygiene — wash your hands, do things like that. It makes a difference. And then it’s also important … when you can’t socially distance and keep that 6 feet, wearing the face mask can help reduce transmission.”

Florida, a battleground state that will host the Republican National Convention in August and a presidential debate in the fall, hit its peak in daily positive cases Saturday, with 4,655 infections. The state recorded 3,862 more cases on Monday, the third-highest total in the past two weeks, and the 25 to 34 age group is the demographic with the most infections.

More than a quarter of Florida’s cases are in Miami-Dade County. The Commission on Presidential Debates announced Tuesday that Miami will host the Oct. 15 presidential debate. Miami Mayor Francis Suarez, however, told POLITICO the debate may not have an audience.

“I can’t see it today being hosted with people in the audience,” he said in a text message. “Impossible to predict where we will be on October 15.”

The surging caseloads in those regions threaten to throttle the Trump administration’s push to reopen the country, raising serious questions about the White House strategy of deferring to the states on health restrictions and other measures as Americans begin to emerge from months of lockdowns. It could also hurt the president’s reelection bid — presumptive Democratic presidential nominee Joe Biden is leading Trump or only narrowly trailing him in recent polling in all three states.

In recent polling in Arizona, both Trump and incumbent GOP Sen. Martha McSally trail their Democratic opponents, Biden and former astronaut Mark Kelly. Democrats need to net three or four Senate seats to win control of the chamber, depending on who wins the White House. Kelly leads by double digits in a Fox News survey released earlier this month, though Biden’s advantage is only 4 percentage points.

Biden has a 6-point lead over Trump in Florida, according to RealClearPolitics average of recent surveys. Bill Clinton in 1992 was the last candidate to lose Florida and still win the presidential election.

Democrats have an uphill battle to unseat Texas Republican Sen. John Cornyn, but in the latest poll of the state this month, the president leads Biden by only 1 percentage point, well within the margin of error in a traditionally red state.

At a rally in Tulsa, Okla., on Saturday — Trump’s first since lockdowns began in March — the president told supporters that he asked his staff to “slow the testing down, please,” because more testing leads to more positive cases. His allies insisted the president was simply joking, but when asked Tuesday if he was kidding, Trump said, “I don’t kid.”

“By having more tests, we find more cases,” he added. “By having more cases, it sounds bad. But actually, what it is, is we’re finding people, many of those people aren’t sick or very little — maybe young people.”

There are indications that young people are one cause of the surging infection rates in some states. DeSantis noted that the median age of Floridians who tested positive has fallen from 65 around March to 35 now. And in Texas, the number of infections is now almost equal among those ages 20 to 29, 30 to 39, 40 to 49 and 50 to 59.

But Florida and Texas’ Republican governors have also acknowledged that the rising numbers are not solely the product of more testing.

“They are testing more than they were, for sure, but they’re also testing positive at a higher rate than they were before,” DeSantis said of young Floridians.

Top Trump administration health officials told a House committee Tuesday that Trump has never asked them to slow down testing. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, said the U.S. will be doing more testing, not less.

“You have to have the manpower, the system, the testing to identify, isolate and contact trace in an effective way so that when you see those increases, you can understand where they’re coming from, and you can do something about them,” Fauci said. “Right now, the next couple of weeks are gonna be critical in our ability to address those surgings that we’re seeing in Florida, in Texas and in Arizona and in other states. They’re not the only ones that are having a difficulty.”