"They can try to hijack another party and get on the ballot, but, look, it's a suicide mission for our country because what it means is that you're throwing down not just eight years of the White House but potentially 100 years on the Supreme Court and wrecking this country for many generations," Priebus said on "Fox News Sunday," anticipating that a conservative third-party candidate would split the Republican vote and ensure a Democrat wins the White House.
"So I think that's the legacy these folks will leave behind. I think it's very dangerous, and there's other ways to get assurances on the things that they're worried about," he said.
The top Republican's comments come as a group of anti-Trump conservatives seek an alternative to the two likely nominees.
Mitt Romney made an unsuccessful effort to recruit Nebraska Sen. Ben Sasse as a third-party candidate, a source with knowledge of the efforts confirmed to CNN Sunday.
Sasse, the freshman Republican, has emerged as one of Trump's foremost critics from the right. Romney and Sasse have talked, the source said, and Romney encouraged Sasse to seriously consider a run.
But Sasse is refusing to enter the race.
"We will decline to comment on the senator's conversations," Sasse spokesman James Wegmann said. "Sen. Sasse has been clear about this when asked before: He has three little kids and the only callings he wants -- raising them and serving Nebraskans. The answer is no."
A Romney spokeswoman declined to comment.
The Nebraska senator's rejection comes as anti-Trump Republicans struggle to find a candidate willing to wage a third-party bid.
Several conservative leaders of anti-Trump efforts, including The Weekly Standard editor Bill Kristol, are polling and reaching out to donors who oppose the presumptive Republican nominee.
"I think there will be an independent candidate," Kristol told CNN's Don Lemon on Thursday. "I think a Republican of integrity and honor who people like me will feel comfortable voting for."
The big problem is that they need a candidate, and haven't found one yet.
For potential candidates like Sasse, appeasing anti-Trump conservatives in Washington comes with risk back home.
At the Nebraska GOP convention, Sasse was rebuked through a resolution that was overwhelmingly approved by Republicans there who argued that his position would only help Hillary Clinton win the White House. Shielding Trump from criticism, the convention also rejected a resolution that would have condemned derogatory remarks toward women and minorities, The Lincoln Journal Star reports
Trump's opponents have also looked outside the political world.
Mark Cuban, the tech mogul billionaire who owns the NBA's Dallas Mavericks, confirmed a Washington Post report that he'd heard from Trump opponents attempting to recruit a candidate. Cuban declined to name the people who were involved.
"My conversations with them were minimal," he said. "They reached out to my right-hand man who is my D.C. guy."