WASHINGTON -- There's now a legal challenge behind the "Never Trump" movement.

Virginia Republican delegate Beau Correll filed a federal lawsuit on Friday seeking the freedom to vote for someone other than Donald Trump at the party's national convention in July.

Beau Correll CBS News

"Donald Trump does not exhibit the judgment, the competency for the highest office in the land," Correll told CBS News.

But state law compels all Virginia delegates to vote "for the candidate receiving the most votes in the primary," even though party rules allocate delegates differently.

Correll, a Ted Cruz supporter, says the law violates his First Amendment rights.

"The government should not compel members of a private association how to vote in that association," Correll said.

Trump won 36 states and amassed more than 13 million votes, a record total. Trump rivals collected more than 16 million votes, also a record.

After Cruz lost, Correll said he considered Trump, but multiple campaign missteps have left him discouraged.

"Donald Trump has anemic poll numbers, anemic fundraising numbers. He can't win by rallies alone," he said.

Correll said he is for literally anybody but Trump.

But David Norcross, a former general counsel to the Republican National Committee and a "Never Trump" skeptic, says it's unlikely any other scenario will play out at the convention.

"There is no other person involved. And [there's] the old saying -- 'You can't be somebody with nobody.'"

A new poll shows more than half of Republicans are dissatisfied with Trump as their nominee. Party leaders believe they can block any procedural moves aimed at derailing Trump, but they are girding for a tough debate and possibly an anti-Trump floor demonstration.