Last-ditch attempts by a group of Republican delegates seeking to stop Donald Trump from becoming the GOP presidential nominee are quickly fading -- and now their fight is facing a federal legal challenge.

At issue is whether delegates to the Republican National Convention in Cleveland are bound to vote for the results of state caucuses and primaries. A group that claims the support of hundreds of convention delegates has been pushing to change Republican presidential nomination rules so that delegates can "vote their conscience" -- reviving a long-simmering debate led by GOP purists who believe that only convention delegates -- not the millions of voters who participated in the primary process -- can ultimately pick a presidential nominee.

Carroll "Beau" Correll, one of Virginia's 49 GOP convention delegates, filed suit in federal court in Richmond on June 24 challenging a state law binding him to the results of the March 1 primary. He's a former federal prosecutor and defense attorney who supported the presidential campaign of Sen. Ted Cruz (R-Tex.). His suit argues that the state law binding him to the primary results violates his First Amendment right to vote his "conscience, free from government compulsion."

Correll wrote in his suit that he believes Trump "is unfit to serve as President of the United States and that voting for Donald Trump would therefore violate Correll's conscience." In his filing, he said that he plans not to vote for Trump on any ballot at the convention in violation of state law.

Eight Virginia Republican delegates supporting Trump sought to intervene in a lawsuit in federal court in Virginia, arguing in their filing that Correll's suit is an "eleventh-hour attack on a longstanding state law" and that he is seeking to "override Virginia voters and instead select his own preferred candidate for the nomination."

John Fredericks, a radio talk show host and Republican delegate from Chesapeake, Va., said that he and seven other delegates intervened with the support of the Trump campaign. Fredericks is vice chairman of Trump's Virginia campaign.

Correll "has an unwillingness to follow the rules," Fredericks said. "This is, in my estimation, a self-aggrandizing, ego-maniacal, publicity-grabbing move that has no chance of success."

"What Mr. Correll is trying to do is to defy the will of 1 million GOP primary voters, 350,000 [of whom] voted for Mr. Trump," Fredericks added. "So all of a sudden, Beau Correll is smarter than 350,000 Virginia Republican voters? This is a sad ploy of a group of people that just don’t want to accept the reality of what voters want. That’s Donald Trump as the nominee."

Spokespeople for the Trump campaign didn't immediately respond to requests for comment. Correll also didn't respond to multiple inquiries. But after filing his suit, he told CBS News, "The government should not compel members of a private association how to vote in that association."

Attempts to change the convention's rules by passing a "conscience clause" so far have failed to pick up enough support. The group pushing for a rule change, Free the Delegates, claims support on the 112-member convention rules committee, but several vote tallies conducted by news organizations including The Washington Post find that no more than 10 members of the committee favor changing the rules.

Meetings to consider proposed changes to the convention's rules are scheduled to be held for up to three days before the convention, beginning on July 14. The convention formally convenes July 18 at the Quicken Loans Arena in Cleveland.

Julie Tate contributed to this report.