In 1993, Mr. Earle prosecuted Ms. Hutchison, who won a special election for the Senate that year, on allegations of misconduct as state treasurer. The case fell apart at the outset of trial, and the judge ordered the jury to acquit Ms. Hutchison. Both Ms. Hutchison and Mr. DeLay claimed they were victims of a politically motivated district attorney.

After Ms. Lehmberg’s arrest, according to the indictment, Mr. Perry threatened to veto state funding for the Public Integrity Unit unless she resigned. He ultimately followed through on the threat, vetoing $7.5 million in state funds. In his veto message, Mr. Perry cited the “otherwise good work” of the unit’s employees but said he could not support continued funding when the public had lost confidence in its boss.

Some speculated that Mr. Perry may have entertained other motives, including the opportunities to hinder a troublesome agency and, if Ms. Lehmberg resigned, to appoint a Republican to an office traditionally occupied by Democrats. “He had a twofer,” said Harvey Kronberg, publisher of The Quorum Report, an online political newsletter. “He had the possibility of neutering it by putting a crony in. Or, if she didn’t resign, the alternative was defund it and make it go away.”

But Mr. DeGuerin, who describes himself as a “Lyndon Johnson Democrat” and is not involved in the governor’s defense, disputes the theory that Mr. Perry would have named a Republican, citing news media reports that Mr. Perry’s office, in behind-the-scenes negotiations, expressed a willingness to name Ms. Lehmberg’s assistant to the post.

State and national Democrats have pushed the story line that Mr. Perry’s funding veto was designed to thwart the unit’s investigation of the Cancer Prevention and Research Institute of Texas, one of the governor’s signature programs. The unit’s investigation, which focused on the awarding of research grants to companies that included Mr. Perry’s political supporters, ultimately resulted in an indictment of a high-level institute official.

Mr. Perry’s lawyers attacked the claim as a misdirection, releasing an affidavit from the unit’s former top investigator in the case who said that Mr. Perry and his staff were never implicated in the case.

Gregg Cox, a 23-year veteran of the district attorney’s office who leads the Public Integrity Unit, says he constantly battles legislative misconceptions about the unit’s work, pointing out that high-profile cases against public officials form only a small part of its portfolio. Of the 425 cases under investigation when Mr. Perry announced his veto on June 14, 2013, he said, only 23 were against public officials or state employees.