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The Hollywood star has hinted that he may run for the state’s highest office in 2022 and has even called it “an honest consideration.”
Now a poll from The Dallas Morning News and University of Texas at Tyler shows that McConaughey as a hypothetical candidate leads Mr Abbot by 44 per cent to 35 per cent.
Back in July Mr Abbott had led Austin-based McConaughey in a similar poll, with 39 per cent to 38 per cent.
The governor has seen his approval rating in Texas drop to 45 per cent in the wake of the controversy surrounding the ban on most abortions after six weeks.
The state has also faced a surge in Covid-19 cases, while Mr Abbott, 63, has banned mask and vaccine mandates.
The poll found that 54 per cent of people believe Texas is “headed off on the wrong track.”
And it is not just the 51-year-old Academy-Award winner that Mr Abbott, who will be seeking his third term in office, may have to worry about.
Democrat Beto O’Rourke, who lost a US Senate race to Ted Cruz in 2018 and has not announced a campaign, has closed a 12 point gap down to five, with 37 per cent of people saying they would vote for him against Mr Abbott.
Axios reported on Sunday that Mr O’Rourke, who was a 2020 Democratic presidential nomination candidate, would make a formal announcement later this year that he intends to run for governor.
“We hope that [O’Rourke is] going to run,” Texas Democratic Party chair Gilberto Hinojosa told Axios.
“We think he’ll be our strongest candidate. We think he can beat Abbott, because he’s vulnerable.”
The poll was conducted between 7 September and 14 September, and surveyed 1,148 registered voters.
The margin of error is 2.9 percentage points.
The pandemic has cost Mr Abbott a significant amount of support in Texas, with his approval rating standing at 59 per cent in March 2020.
More than 60,000 people have died of Covid-19 in the state during the pandemic.