The Sarasota Police Department is investigating, and no charges have been filed against Ziegler as of Tuesday.
The chairman's own co-chair has called for a confidential meeting of party representatives from around the state to take place in just under two weeks, where they will determine Ziegler's future.
Ziegler, however, has dug in, saying an investigation will exonerate him.
"It is not helpful to the mission to have this hanging over his head," Governor Ron DeSantis said Tuesday. "I've said he should step aside."
Ziegler is accused of raping a woman on October 2 after arriving solo for a sexual encounter that was supposed to include his wife, Bridget, a Sarasota School Board member.
There is no mechanism for an automatic removal of the state GOP chair, but party vice chair Evan Power is inviting GOP power brokers to a meeting in Orlando on December 17 to discuss Ziegler's fate.
No one answered Ziegler's door on Monday when a FOX 13 crew stopped by.
Ziegler's lawyer has said, "We are confident that once the police investigation is concluded that no charges will be filed and Mr. Ziegler will be completely exonerated."
On a recorded call as part of the police investigation, Ziegler denied attacking her.
Democrats are calling for the Zieglers' to step down, given their push for the state to adopt rules against teaching gender issues in younger grades.
"They have spent years telling people how to live, what to read and who to be," said former State Rep. Carlos Guillermo Smith.
But, Republicans are piling on too. Sen. Rick Scott said Tuesday, "I don’t see how Christian can continue to successfully act as chairman while this cloud hovers over him."
Pasco GOP Chair James Mallo, who will have a say in the December 17 meeting, said, "The admissions that both he and his wife have made, along with the evidence that has been reported, has caused me to lose confidence in his ability to lead."
The memo about the meeting said they will discuss potential discipline, including a suspension without pay and an internal investigation.
"I think most people acknowledge that it's just an untenable situation," said Gov. DeSantis.
The vice-chair also wrote that he called the special meeting after Ziegler refused to do so.
Sarasota police are investigating, and have requested a judge give them access to a Google Drive, which may contain a recording of the encounter.