CLEVELAND — It is nearing time for the dump-Trump forces to put up or shut up, as they prepare for a final showdown this week on trying to free delegates to the Republican Convention to vote against presumptive presidential nominee Donald Trump.

Party leaders, and a growing number of rank-and-file delegates, say the renegades’ effort is going nowhere: Mr. Trump has solidified his support, struck the right balance with the party’s platform and is in little danger of being ousted.

“Now is the time to stand united as Republicans,” RNC Chairman Reince Priebus told delegates Wednesday as he kicked off the Republican National Committee’s final meeting ahead of the convention. “Now is the time to stop Hillary Clinton and elect Donald Trump.”

Anti-Trump forces will try to defy Mr. Priebus with a last-ditch effort to unbind delegates won by Mr. Trump in the primaries, freeing them to vote their “conscience” — in other words, for someone other than Mr. Trump.

They have little hope of changing the rules in the Rules Committee this week, but if they can get 28 of the panel’s 112 members to support them, they can write a “minority report” that would go to the full convention floor next week, giving all 2,472 delegates a chance to vote on the proposal.

“The minority report will pass,” Kendal Unruh, a Colorado delegate leading the anti-Trump effort, told The Washington Times.

One key test is whether Sen. Mike Lee, a Utah Republican who backed Sen. Ted Cruz during the primaries, gets behind the movement. The widely respected conservative could sway enough delegates to reach the 28 needed to earn a minority report.

But Bruce Ash, chairman of the Rules Committee, said he suspects Ms. Unruh has only a dozen supporters, or far less than she’ll need.

Mr. Ash was once highly skeptical about Mr. Priebus‘ commitment to protecting Mr. Trump’s claim to the nomination, but now says he thinks Mr. Priebus is “100 percent behind Trump.”

Delegates say the New York billionaire also has helped his cause by stringing together a few controversy-free days, and could further placate his critics by tapping an appealing running mate.

Mr. Trump said Wednesday night that the suspense and speculation surrounding his vice-presidential candidate would end Friday morning. “I will be making the announcement of my Vice Presidential pick on Friday at 11am in Manhattan. Details to follow,” he wrote on Twitter.

Mr. Trump has worked in other ways to ease the concerns of Republicans since he wrapped up the nomination in early May. He released a well-received list of potential Supreme Court picks, has proved to be competitive in polling in swing states and deftly handled the party’s platform, inserting his own language about trade deals and immigration policy, while letting religious conservatives pursue social issues fights.

As for the #NeverTrump movement, the real-estate tycoon called those trying to derail his bid within the GOP “a couple of loudmouths,” telling Fox News that even President Reagan had critics.

Some delegates said there is a danger to Mr. Trump should Ms. Unruh’s proposal reach the convention floor.

“I still think it is probably a 20 percent chance it could succeed on the floor, but again it is going to depend a lot of what happens over the coming days,” said Matt Mackowiak, a Texas delegate.

He said delegates will be watching Mr. Trump’s selection of a running mate. Someone like Indiana Gov. Mike Pence or former House Speaker Newt Gingrich would be helpful, while if he picked New Jersey Gov. Chris Christie, “there is going to be a revolt,” Mr. Mackowiak said.

Steve Duprey, a member of the convention rules committee from New Hampshire, said Ms. Unruh’s dump-Trump effort is doomed to fail.

“It goes down by massive numbers,” Mr. Duprey said. “I respect her efforts, but I just don’t see it passing. … I just don’t see the majority of Republican delegates willing to overturn what their voters did in different states. That is not how we roll.”

Shawn Steel, a California delegate, also pointed out that the anti-Trump forces don’t have an alternate candidate to rally around.

“It won’t last very long on the floor,” he said, dismissing Ms. Unruh’s pull within the GOP.

“She is a person that has never been heard of before,” Mr. Steel said. “This is her moment in the sun. She is going to glory in it.”

The Rules Committee has more on its plate than Ms. Unruh’s proposal — but many of those are likely to be swamped by the conscience debate.

Some activists hoped to change the rules to bar paid lobbyists from membership and to drop from RNC representation the five U.S. territories of American Samoa, Guam, the U.S. Virgin Islands and Puerto Rico because they don’t vote in presidential elections.

The activists also wanted to make the national party chairman have slightly less power by having the 168 RNC members name chairmen of the party’s rules, platform, resolutions and other committees rather than the national chairman alone exercising that power.

Mr. Priebus is thought to prefer such proposals not clutter an already difficult convention menu, and Mr. Trump appears ready to go along.

“Trump’s people and I talked this morning, and they are going to follow Reince’s lead on all aspects of rules,” said former Virginia Attorney General Ken Cuccinelli, who originally backed Mr. Cruz for the nomination.

The rules committee could also take up amendments this week that call for, among other things, closed GOP primaries, and switching the states that host the opening primary contests.

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