Republican Atty. Gen. Greg Abbott leads Davis, a state senator from Fort Worth, 29% to 21% in the survey, outside the poll's margin of error. But the race is clearly in the formative stage; half of those sampled were undecided.
Davis, 50, burst onto the national scene in June after leading a filibuster that temporarily stopped passage of strict abortion restrictions. Although the measure was later approved and was signed into law by Republican Gov. Rick Perry, Davis raised more than a $1 million and built a nationwide network of supporters who urged her into the race.
Still, the contest promises to be an uphill struggle for her. Republicans have won more than 100 statewide elections in a row and no Democrat has been elected governor since 1990, when Ann Richards won.
Abbott enjoys a huge financial advantage, with more than $20 million in the bank, and will be able to take advantage of a political and cultural landscape in Texas that tilts decidedly rightward. He faces a primary challenge from Tom Pauken, a former state Republican Party chairman who has little money but a following within the tea party wing of the Texas GOP.
The survey was conducted by the Texas Lyceum, a nonpartisan public policy organization, and has a margin of error of plus or minus 3.47 percentage points.