Democrats See Value in Texas in Candidacy for Governor Mike Stone/Reuters Wendy Davis during a State Senate meeting in July on a bill to restrict abortion in Texas. FORT WORTH - Early this month, Wendy Davis, the unknown Texas state senator who rocketed to fame this summer with her 11-hour filibuster to block an anti-abortion bill, met with strategists of the Democratic Governors Association at their K Street offices in Washington. They were urging her to run for governor next year, even though Texas is not among their realistic targets for flipping a Republican-held executive mansion. All around Ms. Davis, people are encouraging her to get in the governor's race. Whether she can win seems beside the point. Liberal groups in Texas are hungry for her star power to energize the moribund state Democratic Party. Political operatives smell the money that a richly financed Democratic campaign, which early estimates put at $40 million, would direct their way. And national Democrats know a Davis campaign would force the Republican Governors Association to divert millions from more competitive races in Ohio, Florida and Michigan to the Lone Star State. "The R.G.A. would probably have to waste resources there, which is compelling to us," said an official of the Democratic group, who declined to be named because he was not authorized to speak publicly. Ms. Davis, tuning out the self-interested chorus, has spent August engaging in a private inquiry into the viability of a race for which independent analysts put the chances of her success somewhere between a long shot and a pipe dream. On Thursday she said she would announce her decision in a few weeks - a decision she postponed because she is caring for her father, who is hospitalized with complications from surgery, she said in a statement. What trusted advisers, pollsters, fund-raisers and friends are telling her, they said in interviews, is that there is a path to victory, even in Texas, where no Democrat has won statewide office in nearly two decades. "My impression was she was very interested," said Martin Frost, a Washington lobbyist and former Texas congressman whose counsel Ms. Davis sought. You don't get these opportunities very often. She's 50 years old. This is the right time for her. In her most recent public appearance, she sounded very much like a candidate on the verge. She was "very, very seriously considering" a campaign, she told an audience in San Francisco two weeks ago. She added, "I really think hard things are worth fighting for." That sentiment echoed what aides have identified as the best way for Ms. Davis to position herself - as a fighter for her beliefs - and deflect Republican efforts to narrowly define her as a defender of late-term abortion. Researchers presented Ms. Davis with private polling that showed she was better known for her personality than for her positions. They also prepared an analysis of the nearly 900,000 Twitter messages in the 24 hours around her filibuster in June, which temporarily halted a bill to ban abortion in Texas after 20 weeks. A high percentage of those messages focused on her physical ordeal. "Probably the biggest benefit of this filibuster is Wendy is known statewide and she's known as a fighter, and that plays very well in Texas," said Matt Angle, an adviser to Ms. Davis. Republicans are moving swiftly to peg Ms. Davis, whose celebrity was confirmed this month by a Vogue magazine spread, as someone out of step with the state's conservative electorate. "God, I hope she runs, it'll be great," said Dave Carney, a consultant to Attorney General Greg Abbott, the most likely Republican nominee. I don't see her brand of populism, which is beautifully accepted on the Left Coast and the Acela Corridor, being a selling job in Texas. Ms. Davis has sought to broaden her identity, emphasizing a life story that few members of the coastal elites would identify with. Raised by a mother with a sixth-grade education after her father left, she became a single mother herself, living in a mobile home. She worked her way through community college, won a scholarship to Texas Christian University and eventually graduated from Harvard Law School. She served nine years on the Fort Worth City Council before defeating a Republican incumbent for the State Senate in 2008. In Austin, her shoulder-length blond mane inspired jokes that she was the only politician with better hair than Gov. Rick Perry. Much of Ms. Davis's due diligence in eyeing a run has involved sifting the results of past statewide Texas races. The numbers are daunting: President Obama lost the state by 16 points in November. The 2010 Democratic nominee for governor pulled only 42 percent. But Ms. Davis's number crunchers are telling her, in essence, that if she can win her Senate district - much of Fort Worth and its suburbs - she can win statewide. It is the only district out of 31 in the state that is a true battleground, not drawn to protect one of the parties.