CLEVELAND -- A small group of Republican delegates this week could shape whether Donald Trump faces a fight on the convention floor — a dramatic outcome that the presumptive nominee, his campaign and most other party leaders thought he had safely averted.

When the GOP convention rules committee convenes here Thursday, around two dozen delegates are expected to push for a so-called “conscience clause” that would unbind all delegates from state primary results on the first vote. If anti-Trump forces cobble together support from at least 28 delegates on the committee, they would send a minority report forward to the full convention for a vote, likely Monday.

Were this effort to succeed, it would spur a free-for-all on the convention floor, imperiling Trump’s lock on the nomination.

Even as they have publicly dismissed this threat, Republican Party officials have privately treated it seriously, designating a whip team to ensure anti-Trump forces do not reach the threshold needed for a minority report. But the vote may be close. Kendal Unruh, a Colorado delegate leading the conscience clause movement on the rules committee, predicted Wednesday that 30 delegates would back the measure. Trump’s campaign disputed this count.

“Kendal Unruh’s claims that she has enough votes for a minority report are not true,” tweeted Jason Miller, a senior communications adviser for Trump. “The bind/unbind issue is dead.”

Private whip counts by both pro- and anti-Trump factions suggest greater uncertainty, however, putting support for a conscience clause between 20 and 30 delegates, according to a source with knowledge of those counts.

One influential delegate in particular could swing the vote to secure a minority report. Sen. Mike Lee, who sits on the rules committee along with his wife, Sharon, has remained mum on his plans for the vote. But advocates for the conscience clause are optimistic that he will side with them.

The Utah lawmaker “is definitely there in mind, body and spirit,” said one Republican involved in discussions on unbinding delegates, and Lee could be a “deciding factor” if the vote is close by empowering others to follow his lead.

“What he gives people is permission,” the source said. If Lee were to vote in the affirmative, the source added, delegates would have more cover to vote the same without fear of retribution: “If a U.S. senator can do this, so can I.”

One Republican National Committee ally whipping rules committee members against a move to unbind delegates dismissed the suggestion that Lee could wield such clout. "No one gives a hoot what the ‘hired help’ says,” the source said, invoking humorist Will Rogers’s term for members of Congress.

Lee, a conservative freshman senator seeking re-election this year, is one of only two federal elected officials on the panel, in addition to Rep. Steve Pearce of New Mexico. But Lee also has a background as an accomplished attorney and excels at argument.

And he might have a case he hopes to make. Lee has so far held off on endorsing Trump, instead emerging as a vocal critic of the celebrity businessman. In an interview last month with NewsMax, Lee criticized Trump for having made “religiously intolerant” remarks and, during the Republican primary, falsely suggesting that Sen. Ted Cruz’s father was involved in President John F. Kennedy’s assassination.

Typically, the presumptive nominee’s campaign would move swiftly to stamp out any insurrection at the convention. With Trump’s bare-bones campaign lacking this organizational manpower, however, the RNC has instead taken the lead on coordinating with pro-Trump delegates to defeat the minority report — an awkward dynamic for a party that has harbored deep skepticism of its likely standard-bearer. One rules committee member described the RNC and Trump’s team now as “working hand-in-hand” on whipping the committee.

Some anti-Trump forces fear that the party’s involvement could present the most serious threat to their push for a conscience clause, particularly if delegates fear political retribution from GOP officials. And indeed, one Republican whipping against the clause warned: “We have long memories in the Republican Party. I just don’t think it would serve anybody well.”

In addition to the movement to unbind delegates through a vote, a smaller faction on the rules committee plans to argue that delegates are already unbound — an idea the RNC sought to pre-but on Wednesday.

“The RNC rules permit and require the binding of delegates,” said John Ryder, general counsel to the RNC. “Those rules are in effect in this convention. And as long as those rules remain the rules, the delegates remain bound."

But, facing the more pressing question of whether delegates will vote to unbind themselves, Republicans are in a holding pattern.

Morton Blackwell, the Republican national committeeman from Virginia, said Wednesday that a minority report from the rules committee “could very well happen.” But he nevertheless assigned slim odds to Trump losing his hold on the nomination at the eleventh hour.

“Rounded off to the nearest whole number, it would be zero,” Blackwell said. “It might be possible: 0.0001, so that’s a theoretical possibility.”

James Arkin reported from Cleveland, Rebecca Berg from Washington.

Rebecca Berg is a national political reporter for RealClearPolitics. She can be reached at rberg@realclearpolitics.com.