"We are on the cusp of being able to fundamentally change the nature of this disease because of the way in which we're able to get vaccines in people's arms," Biden said. "The last thing -- the last thing we need is Neanderthal thinking that in the meantime, everything's fine, take off your mask, forget it. It still matters."

Abbott's spokeswoman Renae Eze said in a statement that Abbott "was clear in telling Texans that COVID hasn't ended, and that all Texans should follow medical advice and safe practices to continue containing COVID."

"It is clear from the recoveries, the vaccinations, the reduced hospitalizations, and the safe practices that Texans are using, that state mandates are no longer needed. We must now do more to restore livelihoods and normalcy for Texans," Eze said. "The governor's focus has been, and always will be, protecting the lives and livelihoods of Texans."

And his Tuesday moves came too late to mollify some of Abbott's most vocal conservative critics, who accused the governor of attempting to deflect blame after the recent deep freeze left millions of Texans without power and water.

"All he tries to do is hide from the blame," Luther said. "He's trying to take away the focus on the power grid issue, which I think he should have taken a lot more blame for that."

In the latter portion of his second term, Abbott has faced pressure from factions of the GOP that were largely silent in the earlier stages of his governorship.

Abbott has said he plans to seek a third term in 2022, and could face a primary -- with Texas Republican Party chairman Allen West refusing to rule out a possible run.

Some conservative Abbott critics said his Tuesday moves did not go far enough, because the governor left county executives the power to implement their own restrictions.

Democrats also said Abbott's moves were clearly aimed at mollifying his Republican base.

"There's no question he's worried about a primary challenge," said Texas Democratic Party chairman Gilberto Hinojosa.

And, with 2024 on the horizon, Hinojosa said: "He wants to get himself in position to be competitive in the Republican primary, and the only way you can do that is if you take extreme measures along the lines of what Allen West and the far right of the Republican Party has been demanding he do in Texas."

While Abbott has been under siege, potential 2022 rivals, including O'Rourke and former Housing and Urban Development Secretary Julián Castro, have been visible. O'Rourke mobilized his network of supporters to reach out to Texans facing power and water outages after a historic freeze shut down much of the state's power grid last month, and criss-crossed the state himself. Castro has also been a vocal critic of Abbott, and the former San Antonio mayor has reached out to mayors to ask how he could help, Hinojosa said.

"You're going to have a much stronger field of people in this primary than we've had in the past," Hinojosa said, pointing to O'Rourke, Castro and several mayors and county executives as potential candidates.

Though Abbott continues to face heat from the right, he would remain a heavy favorite in next year's governor's race -- a reality that was underscored when other Texas Republicans rallied to his defense Wednesday.

Texas Sen. John Cornyn, responding to Biden's criticism of Abbott, said Biden should not be "preaching to my state about how to handle this COVID-19 virus."

"People in Texas don't really like governments telling them what to do. And I think they've tolerated it for as long as they feel like they had to," he said.