Last month, he met with influential Republican donors, policy experts and operatives whom he had invited to Austin, and he has spent months traveling the world and the country in an effort to repair his image after his mistake-prone 2012 bid for president. The Des Moines Register reported in November that Mr. Perry had been to Iowa eight times and had appeared at 33 events since the 2012 elections, more than any other potential 2016 Republican candidate.

As governor, Mr. Perry was everywhere and into everything. Through his longevity, his thousands of appointees and the force of his personality and ambition, he dominated the state to such a degree that two lawmakers in his own party have proposed bills limiting future governors or other top officials to two consecutive four-year terms. Another sign of his clout and savvy has been the ease with which he has handled perhaps his biggest controversy: the criminal charges he faces accusing him of abuse of power.

A grand jury here in Travis County indicted Mr. Perry last year after he pressed the district attorney, a Democrat, to step down by threatening to cut off state financing to the anticorruption unit in her office. Mr. Perry became the first Texas governor in nearly 100 years to face criminal charges. He and his lawyers deny any wrongdoing, and the case has become more of an annoyance than a crisis for him.

“He took the governor’s office to a higher level,” said Mike Sullivan, 57, a Houston Republican who is the Harris County tax assessor and collector. “I’m a native Texan, a native Houstonian, and I grew up with the belief that the lieutenant governor’s office was the strongest office. I think Governor Perry changed that.”

At the heart of the argument for Mr. Perry’s success as governor is his record on jobs. His office said Texas had added 1.8 million private-sector jobs since January 2001. Employment data from the federal Bureau of Labor Statistics showed the numbers to be accurate. But the data also undercut his claim somewhat. Texas added a similar number of private-sector jobs — 1.4 million — during the tenure of Mr. Perry’s predecessor, Mr. Bush, who served nearly six years compared with Mr. Perry’s 14.

On Thursday, Mr. Perry defended the state’s job growth, telling lawmakers that since December 2007, 1.4 million jobs had been created in Texas, while in that same period, the rest of the nation lost 400,000 jobs. “I have been guided by a simple philosophy: that job creation, not higher taxation, is the best form of revenue generation,” he said.