HARRIS COUNTY (CBSDFW.COM/CNN) — Some cities hit hard by COVID-19 — including one in Texas — are warning more drastic measures could lie ahead as officials try to contain a virus spreading more rampant than ever.

Last week, Houston Mayor Sylvester Turner discussed his proposal to the state’s governor for a two-week shutdown due to the rise in cases. He said the city needed to “reset,” especially as leaders begin conversations about reopening schools.

But Texas Gov. Greg Abbott has said a statewide lockdown is not happening.

“People are panicking, thinking I’m about to shut down Texas again,” Abbott told a Texas television Station Wednesday. “The answer is no. That is not the goal.”

Turner’s proposal parallels what Atlanta Mayor Keisha Lance Bottoms announced last week: that the city’s reopening be rolled back to Phase 1, when residents were ordered home except for essential trips. Georgia Gov. Brian Kemp slammed the decision calling it “confusing” and “legally unenforceable.”

The two leaders in the state have since been clashing on coronavirus guidelines, after Kemp sued the mayor over a mask mandate she ordered for the city.

Los Angeles Mayor Eric Garcetti told CNN Sunday he was on the “brink” of another stay-at-home order, saying things “reopened too quickly.”

“It’s not just what’s opened and closed, it’s also about what we do individually. It’s about the people who are getting together outside of their households, with people they might know. It might be their extended family, it might be friends. They might think because they got a test two weeks ago, that it’s okay. But it’s not.”

The different approaches are just some examples of the conversations between local and state leaders across the U.S. as cases surge and hospital capacities dwindle.

In a month, the U.S. beat its own record of new cases in a day at least nine times. So far, more than 3.7 million Americans have tested positive for the virus and at least 140,534 people have died, according to data from Johns Hopkins University.