Most Democratic voters in Texas would rather see former Rep. Beto O’Rourke (D-Texas) challenge John Cornyn John CornynThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight Senate GOP faces pivotal moment on pick for Supreme Court MORE for his Senate seat in 2020 than continue his run for the White House, according to a new Quinnipiac University poll released Wednesday.

Sixty percent of Democratic and Democratic-leaning voters said the former Texas congressman should abandon his presidential ambitions for 2020 and pursue Cornyn’s Senate seat instead.

Less than half as many respondents — 27 percent — said he should continue his run for the White House, the poll found.

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O’Rourke also placed second among the slate of candidates running for the Democratic presidential nomination, taking 16 percent support of those polled. The figure is roughly half as much as that of frontrunner and former Vice President Joe Biden Joe BidenBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Democratic groups using Bloomberg money to launch M in Spanish language ads in Florida Harris faces pivotal moment with Supreme Court battle MORE's, who notched 30 percent support in the Quinnipiac poll.

Still, Sen. Bernie Sanders Bernie SandersOutrage erupts over Breonna Taylor grand jury ruling Dimon: Wealth tax 'almost impossible to do' Grand jury charges no officers in Breonna Taylor death MORE (I-Vt.) trails O’Rourke in the poll by only 1 point, well within the poll’s 5.8 percent margin of error for Democratic and Democratic-leaning voters.

O’Rourke gained national prominence last year during his closely watched, though unsuccessful, bid to oust Sen. Ted Cruz Rafael (Ted) Edward CruzCruz blocks amended resolution honoring Ginsburg over language about her dying wish Trump argues full Supreme Court needed to settle potential election disputes Press: Notorious RBG vs Notorious GOP MORE (R-Texas). The close race ultimately prompted speculation over whether O'Rourke would jump into the presidential race or mount a second Senate bid in 2020 against Cornyn, who is up for re-election.

O’Rourke announced in March that he would seek the Democratic presidential nomination, quashing hopes of a Senate campaign. So far, a handful of Democrats have jumped into the race to challenge Cornyn, including M.J. Hegar, a retired Air Force major and former House candidate.

But O’Rourke’s campaign has struggled to gain the same kind of traction that his 2018 Senate bid did, lingering in the low single digits in recent national polls.

In recent weeks, he has appeared more frequently on national television and has rolled out a handful of policy proposals, as he looks to regain momentum in the primary contest.

The Quinnipiac poll was conducted from May 29-June 4, among 1,159 Texas voters and includes surveys of 407 Democratic and Democratic leaning voters in the state.