CLEVELAND—Anti-Trump delegates’ last-ditch attempt to deny Donald Trump the Republican presidential nomination failed late Thursday night, after a 15 ½ hour marathon committee session.

#NeverTrump Republicans were pushing a proposal designed to stop Trump in the days leading up to the Republican convention next week. The proposal would unbind Republican delegates from how citizens in various states voted and allow them to vote instead based on their personal consciences.

They weren’t just beaten. They were humiliated, silenced, and shut down.

For weeks, members of the rules committee had been urged to support this rebel effort. One delegate said she had received some 400 emails urging her to support the so-called conscience clause.

It all converged late Thursday night, after an exhausting day of mind-numbing, obscure rules changes. Then came the dramatic moment, a vote that one 40-year rules committee veteran said had "obviously been the subject of more pre-convention publicity than any rules matter ever in living memory."

The incessant campaign of the anti-Trump rebellion rankled some of the delegates committed to the New York businessman. “The people who sent all those emails: It’s over, folks,” proclaimed Iowa delegate Steve Scheffler while the committee debated the proposal. “Let’s get behind our nominee right now.”

The results were disastrous: Not only did the #NeverTrump delegates lose on their issue by an overwhelming number, but the Republican delegates voted to strengthen the binding of delegates.

Using procedures to their advantage, pro-Trump forces on the committee shut down the #NeverTrump effort with ease. In the end, the anti-Trump delegates failed event to get a tallied vote on the “conscience clause”—they were shouted down in a voice vote. They were denied even the chance to debate the initiative.

“This angst isn’t going to go away just because we paper over it with rules,” said Sen. Mike Lee, a rules committee delegate from Utah and a key supporter of the “conscience clause,” urging Trump instead to make the substantive case to Republican delegates for why they should support him.

Not long after his speech, the senator walked out of the rules committee. He told The Daily Beast he didn’t want to comment on what happened inside.

Unbinding proponents never expected to gain a majority of committee members. Instead, the anti-Trump Republicans set their sights on securing 28—a quarter—of the committee’s 112 members, which would have sent the proposal to the convention floor as a “minority report.”

Kendal Unruh, a Colorado delegate leading the unbinding effort, claimed throughout the last week that the anti-Trump Republicans had secured the necessary 28 votes, citing the movement’s internal whip count. A Wall Street Journal survey last week found 20 members open to consider unbinding delegates.

Yet a survey by The Daily Beast, published the day before the failed vote, found only five committee members in support of allowing delegates to vote their conscience.

The anti-Trump Republicans now plan to take their fight to the convention floor next week. Under their interpretation of party rules, delegates have always been free to vote their conscience.

The #NeverTrump movement’s last chance to stop Trump will be through a last-minute challenge on the convention floor, when state delegations participate in the official vote for the presidential nomination.

Usually, each state delegation chairperson simply announces the state delegates’ vote count, as it has been pre-assigned by party rules. But an anti-Trump delegate could contest his or her state’s vote count and ask for, essentially, a redo of votes while on the convention floor—and the delegates hope to switch their votes away from Trump during the recount.

“Strictly speaking, the rules as they exist now support the fact that we are unbound,” Eric Minor, an anti-Trump Washington state delegate, insisted on Thursday afternoon.

Anti-Trump forces have tried nearly every tool in their arsenal to deny Trump the Republican nomination—but at this late stage in the process, the most they could cause is a little trouble. On Thursday night, they barely managed that.

--Andrew Desiderio contributed to this article.