Texas State Senator Wendy Davis (D) rose to national prominence last week with her successful 11-hour filibuster of a strict abortion law.

However, despite a surge of interest in Davis' political future, the Texas lawmaker is still a long shot to become the state's next governor, according to a PPP poll released Tuesday.

Davis has doubled her in-state name recognition since January, such that 68 percent of voters now know who she is. Yet in a head-to-head matchup with Texas Gov. Rick Perry (R), Davis still trails by a sizable 14 points, 53 to 39 percent.

That's actually a worse showing for Davis than what PPP found when it polled the same question back in January. At that time, Davis trailed Perry by just a six-point margin, 47 to 41 percent.

Further, despite the debate Davis' filibuster spawned over women's issues and reproductive rights, Perry actually leads her among female voters, 49 to 43 percent.

"Wendy Davis made a strong first impression on Texas voters last week," said PPP President Dean Debnam. "But the chances that the state turns blue in 2014 still look pretty slim."

Perry's approval rating has improved significantly over the first half of the year. He's still underwater, with 50 percent of voters saying they disapprove of his job performance versus 45 percent who say the opposite. But that's much better than January, when that split was 54 to 41 percent.

While Texas' abortion debate has grabbed national headlines and drawn a wave of support for Davis across the web, Texans remain evenly split on the issue. Forty-five percent of voters say they support Davis' filibuster, while 40 percent say they do not. At the same time though, 43 percent say they support Perry's decision to call a special legislative session to ram through the abortion bill Davis blocked, while 44 percent oppose.

Also working against Davis is the state's heavy Republican tilt. Perry won re-election in 2010 by double-digits despite being a relatively unpopular governor. Mitt Romney won there last November by a 16-point spread.

Perry will announce on Monday whether he plans to seek another term. Attorney General George Abbott, a Republican who says he may join the race, also leads Davis by a 48 to 40 percent split in the new PPP poll.