The United States' alarming rise in coronavirus cases isn't due to increased testing — particularly not where cases have grown fastest over the last month, Axios' Andrew Witherspoon and I report.

Why it matters: The U.S. doesn't yet know what it looks like when a pandemic rages on relatively unchecked after the health system has become overwhelmed. It may be about to find out.

The big picture: The number of tests completed in the U.S. is going up, which is a good thing. But the number of new cases is increasing faster.

• The situation varies state by state, but the gap between testing and cases is generally largest in the cases with the fastest-growing coronavirus outbreaks, like Florida and Texas.
• But in some places, like the District of Columbia and New York, testing has grown faster than new cases — a good indicator that these outbreaks are under control.

My thought bubble: Even if testing did explain why America's official coronavirus caseload has doubled over the last month, that would be little cause for comfort; it'd only indicate that we have a worse problem than we'd thought.

• But the reality is that states like Arizona, Florida and Texas are struggling to meet the demand for coronavirus tests, meaning the pandemic is already outpacing those states' ability to respond to it.

See the trends in all 50 states.

A record 8,181 coronavirus patients were hospitalized yesterday in Texas, and officials in major cities warned that hospitals' intensive care capabilities could be overwhelmed within weeks, the Texas Tribune reports.

The big picture: New York hospitals never became so overwhelmed that patients were abandoned in hallways. But the situation became dire after lockdowns were in place, and it was mostly a matter of riding out the storm.

• In Texas and elsewhere, people remain free to move around and thus keep spreading the virus.

What they're saying: Austin Mayor Steve Adler told the Austin American-Statesman yesterday that the city's hospitals could be overwhelmed in the "next 10 days to two weeks."

• The San Antonio Express-News reported that San Antonio's hospitals could be overrun in a week or two, with coronavirus hospitalizations rising by 55% in that area's trauma service region over the last week.
• In the Rio Grande Valley, 10 of 12 hospitals had already reached capacity by Saturday.

The bottom line: "Like New York City in March, the Houston hospitals are experiencing a steep rise in caseloads that is filling their beds, stretching their staffing, creating a backlog in testing and limiting the availability of other medical services," the New York Times reported over the weekend.

• Health care workers are falling sick, and hospitals are struggling to replace supplies.
• However, doctors have learned more about how to treat patients since March. And so far, Houston patients are younger, healthier and not as sick as New York's.

President Trump signed off on Saturday to give businesses another five weeks to apply for funds through the Paycheck Protection Program.

The Trump campaign will be providing face masks and hand sanitizer for all attendees at an upcoming rally Saturday in Portsmouth, New Hampshire.

Arizona's intensive care units were at 91% capacity on Friday, the Arizona Department of Health Services reports.

Stop AAPI Hate announced there have been 832 self-reported incidents of discrimination and harassment against Asian Americans and Pacific Islanders in California in the last three months.

New Jersey Gov. Phil Murphy (D-N.J) on NBC's "Meet the Press" Sunday called for a national face mask mandate to help prevent the spread of the coronavirus.

A group of 239 scientists in 32 countries is calling for the World Health Organization to revise its recommendations to account for airborne transmission as a significant factor in how the coronavirus spreads, the New York Times reports.

Mexican leaders are calling for stronger enforcement on its northern border as the number of coronavirus cases in the southwestern U.S. continues to rise, The Washington Post reports.

Still not convinced the pandemic is worsening? Here's more proof: At least 15 states broke their single-day coronavirus infection records this week, according to state health department data reviewed by Axios' Orion Rummler.

• On Sunday, Alabama broke its daily infections record with 298 new cases.
• On Monday, California recorded 9,480 new cases, and South Carolina found 1,738 new cases.
• On Tuesday, Oklahoma counted 585 new infections.
• On Wednesday, 2,946 new cases were found in Georgia, Arizona had over 4,800 new cases, West Virginia reported 78 confirmed and probable cases, and Montana reported 67 new infections.
• On Thursday, Oregon recorded 375 new cases, Arkansas reported nearly 900 new cases, and Tennessee had 1,575 cases.
• On Friday, North Carolina broke the record it had set on Wednesday for its highest single-day infections (1,843) with 2,099 new cases. Idaho counted 401 infections on Friday, breaking the record it set on Tuesday (365).
• On Saturday, Florida reported 11,445 new infections and broke the record it had set on Thursday (10,109). Texas counted 8,258 cases, breaking its record from Wednesday (8,076).

What they're saying: "Right now, if you look at the number of cases, it's quite disturbing. We're setting records, practically every day, of new cases in the numbers that are reported. That clearly is not the right direction," NIAID director Anthony Fauci told medical journal JAMA on Thursday.

Go deeper: Coronavirus cases skyrocketing among communities of color

Shot: "Hospitals are now facing the greatest financial crisis that we have ever faced in our history," American Hospital Association CEO Rick Pollack told CNBC last week, Axios' Bob Herman writes.

Chaser: That same day, another AHA executive said on a Cowen research and investment conference call that many hospitals are back to operating at 90% of historical volumes, and "although the recent surge of positive COVID-19 cases in Texas and Arizona has given him some cause for concern, he stated that the pace of procedure volume recovery has been encouraging and trending in a positive direction."