HALTOM CITY, Tex. — Exactly 100 days after the legislative filibuster that defied the Republican establishment and turned her into a Democratic star, State Senator Wendy Davis announced Thursday that she would run for governor, opening an underdog campaign to lead a state that last sent a Democrat to the governor’s mansion nearly 23 years ago.

Standing before an estimated 2,000 supporters at a modest redbrick arena in the working-class community where she received her high school diploma in 1981, Ms. Davis tied her candidacy to both the challenges that brought her to this unlikely campaign and to the promise of a state eternally entranced by its own mythology.

“We know that Texas is more than a state,” she said. “Texas has always been a promise. The promise that where you start has nothing to do with how far you can come. In Austin today, our current leadership thinks that promises are something you just make to the people who write the big checks.”

Ms. Davis’s speech, perhaps reflecting the difficulties of a Democrat in a conservative state, focused as much on her personal story as on her political agenda. Her mother, she has said, was a single parent with a sixth-grade education. Soon after Ms. Davis graduated from high school she got married, divorced and became a single mother herself at the age of 19, living in a trailer with her daughter, Amber, and, she told the audience, coming home to find the power turned off or her phone disconnected.