Washington (CNN) A coalition of Republican delegates is mounting a last-ditch effort to block Donald Trump from obtaining the GOP nomination by pushing for a "conscience clause" that would allow delegates to vote against the presumptive nominee.

Kendal Unruh, a Colorado delegate, organized a call with dozens of other delegates Thursday night to discuss ways to block Trump at the convention. The group, Unruh says, marks the coalescing of disparate "pockets of resistance" -- including backers of Sen. Ted Cruz, Sen. Marco Rubio and Ohio Gov. John Kasich -- which had been opposing Trump with little success.

"This is a coalition of Kasich, Cruz and Rubio (supporters) and we are all agreeing on one goal, which is: Anybody but Trump," Unruh said Friday.

Any stop-Trump effort would be nearly impossible to pull off at this point in the election cycle. But moves such as Thursday's call demonstrate that Trump's opponents inside the GOP are trying to organize more effectively. And, perhaps more importantly, it reflects the mounting anxiety inside the party about Trump's candidacy amid polls that show him badly trailing presumptive Democratic nominee Hillary Clinton. His comments in the aftermath of the Orlando attacks -- and his earlier criticism of a judge because of his Mexican heritage -- have alarmed many in the GOP.

Trump dismissed the effort Friday, suggesting it would be "illegal" if the delegates tried to thwart the binding of the delegates.

"I have tremendous support and get the biggest crowds by far and any such move would not only be totally illegal but also a rebuke of the millions of people who feel so strongly about what I am saying," Trump said in a statement. "People that I defeated soundly in the primaries will do anything to get a second shot -- but there is no mechanism for it to happen."

The Republican National Committee, which has largely aligned with the Trump campaign, also dismissed the effort Friday.

"The extent of this effort is a bunch of random people tweeting about it, full stop," said Sean Spicer, RNC chief strategist.

Later Friday, Spicer tweeted a short statement: "Donald Trump bested 16 highly qualified candidates and received more primary votes than any candidate in Republican Party history. All of the discussion about the RNC Rules Committee acting to undermine the presumptive nominee is silly. There is no organized effort, strategy or leader of this so-called movement. It is nothing more than a media creation and a series of tweets."

Unruh, a member of the Republican convention Rules Committee, said she is lobbying others to sign on to her proposal. She would need 56 other supporters from the 112-member panel, which will determine precisely how Republicans select their nominee in Cleveland.

The group, Unruh said, has dubbed itself "Free the Delegates 2016" -- a nod to another rules committee member, Curly Haugland, who has been arguing that delegates should not be forced to vote for Trump.

The renewed push to block Trump from securing the nomination comes after two incredibly choppy weeks for the presumptive nominee, following his comments on federal Judge Gonzalo Curiel and his promise to pursue a ban on Muslims entering the country in response to the Orlando terror attack.

Steve Lonegan, a New Jersey Ted Cruz backer and former U.S. Senate candidate who was on the organizing call Thursday night, said that Republicans who do not believe Trump represents what the party stands for have a "moral obligation" to stop him in Cleveland next month.

"I will tell you, about every two hours people contact me about how to join this effort," said Lonegan said. "This has never been done before, so there's no textbook on how to do it. So we're building an organic effort, state by state, to convince members of the Rules Committee to sign onto a rule that unbinds the delegates to vote their moral conscience."

Efforts to oust Trump in Cleveland appeared to ebb after Weekly Standard editor Bill Kristol floated David French as his vaunted third-party option. But the movement to ouster Trump gained new steam after the fallout from the past two weeks.

A group of people -- including Eric O'Keefe, a former top fundraiser for Cruz -- recently formed a group they're calling " Delegates Unbound, " an effort to convince delegates that they have the authority and the ability to vote for whomever they want. A source working with the group told CNN that they are going to try to not only directly communicate with the delegates but also try to raise money to buy TV ads.

Unruh has moved out in front publicly on the issue, but top-level donors and operatives have been re-examining their options for removing Trump behind the scenes as well.

They come after efforts by top Republican donors and party leaders to tamp down Trump's language appear to have failed. Unruh mocked those very efforts to rein in Trump, saying they would end up helping her cause.

"This will be an absolute success once that tranquilizer they sedated Trump with wears off," Unruh said.

. said Republicans who don't want to support Trump by saying no one should betray their conscience. Trump opponents have been getting some high-profile cover as well House Speaker Paul Ryan said Republicans who don't want to support Trump by saying no one should betray their conscience.

"The last thing I would do is tell anybody to do something that's contrary to their conscience," Ryan told NBC's Chuck Todd in an interview on "Meet the Press" that will air Sunday. "Of course I wouldn't do that."

As confusion continued to swirl about the pending nomination of Trump, Republican National Committee Chairman Reince Priebus announced Friday the selection of four party loyalists who will fill vital posts in the convention in Cleveland.

Priebus tapped RNC vice chairwoman Enid Mickelsen and former George W. Bush political director Ron Kaufman to co-chair the convention Rules Committee. And he also tapped former RNC Chairman Haley Barbour -- a trusted power player among establishment Republicans -- to lead the convention's Committee on Permanent Organization with Wisconsin RNC Committeewoman Mary Buestrin.

CNN's Dana Bash contributed to this report.