Rep. Beto O'Rourke Beto O'RourkeJimmy Carter says his son smoked pot with Willie Nelson on White House roof O'Rourke endorses Kennedy for Senate: 'A champion for the values we're most proud of' 2020 Democrats do convention Zoom call MORE (D-Texas) on Thursday ruled out a 2020 presidential run if he wins in November against incumbent Texas Sen. Ted Cruz Rafael (Ted) Edward CruzThe Hill's Morning Report - Sponsored by Facebook - Trump previews SCOTUS nominee as 'totally brilliant' Cruz blocks amended resolution honoring Ginsburg over language about her dying wish Trump argues full Supreme Court needed to settle potential election disputes MORE (R).

The Texas Democrat, whose national prominence rose in recent months, did not however specifically rule out the possibility of running if he is defeated in November during a CNN town hall.

“The answer is no,” he told an audience member who asked if he foresees himself running for president. “Our children are 11, they’re 10, and they’re 7 years old. We’ve told them we’re going to take these almost two years out of our life to run this race, and then we’re devoted and committed to being a family again.”

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“I mean, let me put it this way,” he added when pressed by CNN's Dana Bash. “I promise to you, and most importantly, to the people of Texas, that I’ll serve every single day of a six-year term in the United States Senate and I won’t leave this state to go run for president.”

O'Rourke added that he would be "back in El Paso" if he doesn't win, though not specifically saying if losing would affect his 2020 plans.

Rep. Beto O'Rourke gives @DanaBashCNN a "definitive no" as to whether he would run for president.



"I promise to you and most importantly the people of Texas that I'll serve every day of a six-year term in the United States Senate," O'Rourke said. #TexasTownHall pic.twitter.com/J3pvy8EaKd — OutFrontCNN (@OutFrontCNN) October 19, 2018

O'Rourke's popularity following the a video on social media showing him defending NFL players' right to protest led to some speculation whether the 46-year-old could be a potential future contender for higher office in the Democratic Party.

He currently trails Cruz in the state's Senate race by single digits, according to recent polling of the race, but reported a massive $38 million fundraising haul for the most recent quarter of 2018.