The University of Texas and Dallas Morning News survey discovered that McConaughey is preferred in both one-on-one matchups, yet Abbott would prevail in a three-way race.
McConaughey, who lives in Austin, has teased a run for governor for months though he has not announced whether he would make one as a Republican or a Democrat.
The 52-year-old Oscar-winning actor keeps his political beliefs close to the vest, though his previous comments imply that he is Moderate to Conservative-leaning.
In the new survey, respondents asked regarding a hypothetical matchup between Abbott and McConaughey preferred the actor, 43 percent to 35 percent, with the rest stating they were uncertain.
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When questioned regarding a race between McConaughey and O'Rourke, who recently declared his plan to run next year, McConaughey prevailed 49 percent to 27 percent.
Although in a three-way race with all candidates running, the plurality favored Abbott, who earned 37 percent support to McConaughey's 27 percent and O'Rourke's 27 percent.
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Just 40 percent announced they wanted McConaughey to run for governor, with 33 percent voicing opposition and the rest stating it didn't matter to them.
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McConaughey, praising from a small town in deep Texas and raised in a religious family, has hinted at a possible third-party run, stating he has problems with both parties.
"Each party is claiming to be a democracy itself, and in doing so can't much tell you what they're about," he told AFP earlier this month.
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He went on: "You got to go 'left' sometimes, you got to go 'right.' There are people on the so-called right and the so-called left that are better people for the job at hand at different times."
"Look, it's been discussed. It's a possible avenue," McConaughey announced when asked regarding a run for governor.
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"I would call myself aggressively centrist. Not because that's the place of gray and compromise... I think today it's a daring space. It's the space of outlaws."
If McConaughey does choose to run for the Lone Star State's top office, he will require to file by a December 13 deadline.
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Pushed on whether he has taken key early steps like hiring campaign staff or fundraising, he responds with a stock line: "I'm not, until I am."
"It's something I'm giving great consideration...there's some wonderful sacrifices for the awesome position."
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O'Rourke's announcement earlier this month that he will seek the governor's office kicks off a third run for office in as many election cycles.
He broke into the 2020 Democratic Presidential Primary as a party phenomenon though he dropped out just eight months later as money and fanfare dried up. In 2028, his bid for U.S. Senate was defeated by incumbent Republican Ted Cruz.
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