
However, at a Monday press conference in San Antonio, the governor also said people should be prepared to see the number of Texans testing positive take a dramatic upswing as more testing comes online and as community spread increases.
"You're going to see an exponential increase in the number of people testing positive on a daily basis, " Abbott said.
At press time, health officials have reported at least 69 cases of COVID-19 in the Lone Star State. More than 200 Texans have been tested and 300 more are currently undergoing testing, the governor said.
At the press conference, San Antonio Mayor Ron Nirenberg announced a new state of health emergency for the city, which includes limiting gatherings to no more than 50 people — a guideline established by the Centers for Disease Control.
Federal, state and local officials, working in conjunction with private health care providers, are in the process of setting up mobile testing sites around the state, Abbott said.
"By the end of this week, anyone who needs a COVID-19 test will be able to get a COVID-19 test," Abbott said.
However, he cautioned that people will need a doctor's order to use the facilities. Groups prioritized for testing include first responders and health care providers; high-risk groups such as the elderly and those with weakened immune systems; and people displaying symptoms that could be something other than a cold or the flu.
"You can't just drive up to this like you'd drive up to a Whataburger and order a cheeseburger," Abbott added. "You can't just drive up to this and order a COVID-19 test."
The governor's comments come as the Trump administration faces a chorus of condemnation for its slow rollout of test kits to deal with the pandemic.
On Thursday, Dr. Anthony Fauci of the National Institutes of Health said the U.S. was caught flat-footed when it came to being able to test for the virus.
“The system is not really geared to what we need right now,” he said. “That is a failing. It is a failing, let’s admit it."
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