Abbott is threatening to cut off state funding to Travis County Sheriff Sally Hernandez after she announced Friday she would reduce her department's cooperation with federal immigration authorities when they request an inmate be flagged for possible deportation. If she continues with the policy, Abbott suggested a more serious punishment. 

"We will remove her from office," Abbott said in an interview on Fox News.

It was not immediately clear how legislation would remove Hernandez from office. She won her election last year. Sanctuary cities opponents view such officials' immigration policies as a violation of their oaths of office. 

The Fox News interview appears to be the first time Abbott has suggested officials like Hernandez could lose their jobs under sanctuary cities legislation. Abbott is expected to prioritize the legislation in his State of the State address on Tuesday. 

Hernandez's office did not have an immediate comment on Abbott's remarks. The governor's comments, however, quickly drew ire from other Democrats, with the state party saying in a statement that Abbott was "launching a new assault on the will of Texans."

"I don’t know how the governor would suggest to do that," state Rep. Rafael Anchia, D-Dallas, said at a news conference that was called to push back on sanctuary cities legislation. "Typically people are elected by the voters. Democracy, in fact, works."

"And unless the governor wants to be king and remove people from office unilaterally, then I think the people of Travis County will have an opportunity to speak on the sheriff, the governor and all other elected officials when they stand for re-election," Anchia added. 

By the end of Wednesday morning, the Texas Senate GOP caucus released a letter, signed by all 20 GOP senators, backing up Abbott in his showdown with Hernandez. The letter did not address Abbott's proposal to remove officials like her, but told Hernandez her policy "is a reckless and blatant political stunt that not only prohibits law enforcement officers from doing their job, but also jeopardizes the safety of the citizens of Travis County."