They understand that getting on the ballot at this late stage will be a challenge but insist they can overcome that with the right candidate and resources.
Their continued work to halt Trump, the presumptive Republican nominee, comes as Rep. Adam Kinzinger, a prominent GOP congressman from Illinois and Iraq War veteran, has decided to pass on an independent bid.
Adam Kinzinger, 38 and in his third House term, would have considered mounting an independent bid had the barriers to an independent run not been so daunting. His pondering of the matter reflects ongoing efforts by GOP forces opposed to Trump and Hillary Clinton, the likely Democratic standard-bearer. They have searched feverishly in recent weeks for a candidate of stature to make an independent conservative White House bid. But like Kinzinger, no potential candidate has yet bitten.
Kinzinger, previously a prominent surrogate for former Florida Gov. Jeb Bush, would have undertaken a third party run "literally to save the union," according to a source familiar with his thinking, because both Clinton and Trump scare him. But Kinzinger does not think the infrastructure exists to get on the ballot in a number of states at this relatively late date.
Yet conservative leaders over the weekend continued to profess confidence that they would successfully recruit a candidate. Bill Kristol, editor of The Weekly Standard and a prominent conservative critic of Trump, tweeted late Sunday that "there will be an independent candidate -- an impressive one."
Two people floated by Kristol have said they won't run -- Mitt Romney, the 2012 GOP nominee, and freshman Sen. Ben Sasse of Nebraska.
Two sources close to Mitt Romney told CNN he still will not go so far as to to run as an independent. One of the sources said, "No, no, no, no, no. I promise you. No."
Sasse is still a no as well, according to a source close to the senator.
The efforts to recruit an independent conservative candidate come as Republican establishment figures increasingly coalesce around Trump's bid. Since effectively securing the nomination on May 3 with his Indiana primary win, more members of Congress have voiced support for Trump, as have former Republican rivals like Sen. Marco Rubio of Florida.
Kristol said in an email to CNN no announcement is imminent. He would not say more about who may be considering this third party run.
But logistical hurdles to an independent bid are increasing. Ballot deadlines for independent candidates have either passed or soon will. Though Never-Trump forces think ballot access challenges can be overcome with the right candidate and resources. In Texas the deadline for getting on the ballot has already passed, but a write-in-campaign or lawsuit could potentially open up room for a new candidate. Another looming ballot access deadline is North Carolina, on June 9, which a source suggested would also likely be missed.
Sources familiar with efforts by Kristol and other Never-Trump Republicans say they have done extensive polling and gathered other private data, and talked to potential candidates and financial backers.
Kristol's efforts have earned the wrath of Trump, who on Sunday night trashed him in a series of tweets, warning that an independent candidate would serve as a "spoiler" for Republicans in the fall, and their future hold on institutions like the Supreme Court.
On Monday evening Kristol fired back, tweeting:
"I'm traveling, so hadn't realized I'd so upset @realDonaldTrump. I'm sorry the mere mention of an independent candidate has so unnerved him."