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Officials in states with surging coronavirus cases issued dire warnings and blamed outbreaks on early reopenings Sunday as the seven-day average for daily new cases in the United States reached a record high for the 27th straight day.

“We don’t have room to experiment, we don’t have room for incrementalism when we’re seeing these kinds of numbers,” said Judge Lina Hidalgo (D), the top elected official in Harris County, Tex., which encompasses the sprawling Houston metro area. “Nor should we wait for all the hospital beds to fill and all these people to die before we take drastic action.”

Here are some significant developments:

  • The University of Washington reported that at least 121 students have tested positive for the virus and that 112 of them lived in fraternity houses near the Seattle campus. The university’s medical school has erected a pop-up testing site near the school’s Greek Row.
  • Thirteen states reported new highs in their seven-day case averages, with Montana, Delaware and Alaska experiencing the biggest percentage change from their past records. West Virginia also set a record number of daily cases, with 130.
  • South Carolina, Texas, Arizona, Nevada and California reported record numbers of current covid-19 hospitalizations. The country’s seven-day average of new deaths fell to 485, down from 562 on June 28, but health experts cautioned that the count of infections would soon drive the number back up.

The somber numbers have caused frustration among local leaders, who say they have had to grapple with conflicting orders regarding the pandemic and frequently changing guidelines from governors and the White House as they try to curb sharply rising infections.

After Texas reported another single-day record for new coronavirus cases over the weekend, Austin Mayor Steve Adler (D) told CNN’s “State of the Union” that there won’t be enough medical personnel to keep up with the spike in cases if the rate of increase continued unabated in his city.

“If we don’t change this trajectory, then I am within two weeks of having our hospitals overrun,” he said, adding that intensive care units in the city could be overflowing within 10 days. He said he was not sure that Texas needed a statewide shelter-in-place order but that he wanted the authority to impose one locally.

Houston Mayor Sylvester Turner (D) echoed Adler’s concerns. The hospitals in his city face staffing shortages as demand for ICU beds increases exponentially, he said on CBS News’s “Face the Nation.”

“In fact, if we don’t get our hands around this virus quickly, in about two weeks, our hospital system could be in serious, serious trouble,” Turner said. Demand for testing has also outstripped the city’s capacity, he said, and the positivity rate has soared from 10 percent a month ago to 25 percent recently.

In an interview with ABC News’s “This Week,” Hidalgo said she had been stripped of authority to issue stay-at-home orders in Harris County, as she did in the early weeks of the outbreak, after Gov. Greg Abbott (R) decided to move forward with an aggressive reopening plan in the spring. All she could do now was issue “recommendations,” which were nowhere near as effective, she said.

“As long as we’re doing as little as possible and hoping for the best, we’re always going to be chasing this thing, we’re always going to be behind, and the virus will always outrun us,” Hidalgo said. “And so what we need right now is to do what works, which is a stay-home order.”

In Florida, new coronavirus cases exceeded 10,000 in a day on Sunday for the third time in the past week, after the state posted a record high of 11,458 the previous day. The new infections pushed the state’s total caseload past 200,000, a mark passed by just two other states, New York and California.

Miami Mayor Francis X. Suarez (R) said it was “clear that the growth is exponential at this point.”

“There’s no doubt that when we reopened, people started socializing as if the virus didn’t exist,” he told ABC News. “It’s extremely worrisome.”

Food and Drug Administration Commissioner Stephen Hahn said it was “too early to tell” whether the Republican National Convention could be held safely in Jacksonville, Fla., next month. “We’ll have to see how this unfolds in Florida and elsewhere around the country,” he told CNN.

Phoenix Mayor Kate Gallego (D) attributed soaring case numbers in Arizona to the state’s decision to resume business as usual before the virus was under control. She noted that young people who ignored health guidelines had probably led the explosion in cases.

Gallego said federal officials had dismissed her requests to conduct community-based testing in the area after people reported waiting in line for six hours at some testing sites. “We were told they’re moving away from that,” she said, “which feels like they are declaring victory while we’re still in crisis mode.”

In Greenville, S.C., the nightclub where two were killed in a shooting early Sunday had violated crowd restrictions enacted because of the pandemic, County Sheriff Hobart Lewis told the Greenville News. In fact, he said, the club was not allowed to be open and officials were considering revoking its liquor and business licenses.

New Jersey Gov. Phil Murphy (D), whose state was battered by the virus in April, called for a national mask-wearing requirement.

“We went through hell. We cannot afford to go through hell again,” he said on NBC News’s “Meet the Press.” “We need a national strategy, I think, right now, and masking has got to be at the core of that.”

The warnings came after President Trump said Saturday that his administration had made “a lot of progress” in combating the pandemic. Speaking at an Independence Day event on the White House lawn, he said the country had “learned how to put out the flame” of the coronavirus.

Trump continued to assert that testing had inflated new case numbers — a claim contradicted by rising positivity rates and widely disputed by epidemiologists — and said the country was making progress on developing therapeutics and a vaccine.

Public health experts have stressed that the recent surge in cases is not the result of expanded testing capacity alone. “When the virus is under control, testing doesn’t uncover more cases. It’s a tool for keeping the epidemic at bay,” said former FDA commissioner Scott Gottlieb, who served under Trump.

Gottlieb voiced doubts about the country’s ability to slow the pandemic, saying waves of infection would probably persist through the rest of the year. The situation was at least as bad as it was during the height of the outbreak in New York earlier this year, he said, except that the country was not dealing with multiple centers of infection.

“We’re not going to really be able to crush this virus at this point because there’s just so much infection around,” he said on “Face the Nation.” “We really don’t seem to have the political will to do it.”

Elise Viebeck contributed to this report.