A majority of voters polled said President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE should face a Republican primary challenger in 2020, according to a new American Barometer survey.

The poll, conducted by Hill.TV and the HarrisX polling company, found that 72 percent of all respondents said they wanted Trump to face a primary opponent, compared to 28 percent who said they wanted him to be the nominee without facing a GOP challenger.

The party breakdown found that 43 percent of Republican voters in the survey want a GOP candidate to run against the president, a feeling shared by 78 percent of independents and 91 percent of Democrats.

"Those aren't that great numbers for President Trump," Republican pollster Conor Maguire told Hill.TV's Joe Concha on "What America's Thinking." "There seems to be a lot of Republicans that are really not sold on reelection."

Ohio Gov. John Kasich, Sen. Ben Sasse (R-Neb.), and Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeHow fast population growth made Arizona a swing state Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden MORE (R-Ariz.) are all considered potential primary challengers to Trump.

Flake last week did not rule out a presidential run, while pointing to Sasse and Kasich as possible candidates.

"I've not ruled it out. I've not ruled it in. Just, somebody needs to run," Flake told reporters.

"But I hope somebody does just remind people what it means to be conservative and what it means to be decent. We've got to bring that back," he added. "If we're going to be a relevant party in the future then we've got to be a decent party."

The American Barometer survey was conducted Nov. 9-10 among 1,000 registered voters. The sampling margin of error is plus or minus 3.1 percentage points.