Cleveland (CNN) In the weeks before Republicans descended on Cleveland, the band of conservative delegates fighting against Donald Trump promised a scrappy but ardent effort to take the convention by storm.

Two days into the preliminary meetings, there's little sign the anti-Trump movement is taking hold.

Republican National Committee members and delegates gathered in Cleveland for this week's battle have thus far largely brushed aside the effort to change the convention rules and allow delegates to vote for any candidate.

"Whether you supported Donald Trump along the way or not: He. Is. Our. Nominee," said RNC Rules Committee Chairman Bruce Ash Tuesday.

Others have gone further -- in one scene Tuesday afternoon, a key RNC member confronted an anti-Trump organizer he said was behind radio ads attacking him.

Asked Monday if he was worried about the anti-Trump delegates, as he attempts to run a smooth convention, RNC Chairman Reince Priebus said, "I'm not. I'm not. I'm hearing less and less of it actually. So I think the unbind stuff has died off considerably over the last 10 days or so."

The anti-Trump coalition -- including groups Free The Delegates and Delegates Unbound -- won a small victory in a federal court in Virginia this week, and the group's leaders have kept up their push since arriving in Cleveland.

Organizing calls led by Colorado delegate Kendal Unruh, leader of Free The Delegates, described a coordinated plan to win enough supporters to rewrite the convention's very rules to Dump Trump.

Ironically Ted Cruz, whom many of the anti-Trump delegates ardently support, appeared to hurt their cause last week after he met with Trump in Washington and agreed to speak at the convention. (Cruz has not endorsed Trump, however.)

"By co-opting Cruz and giving him a speaking slot, the Trump campaign sucked some of the wind out of the anti-Trump sails," said CNN delegate analyst and former Marco Rubio campaign aide Will Holley.

Maneuvering behind the scenes

While anti-Trump advocates try and gain traction, Republican National Committee members Tuesday essentially decided to ignore the issue.

The RNC rules panel voted down a proposal from RNC Oregon Committeeman Solomon Yue that would have pushed off any anti-Trump measures from taking effect until 2020.

Yue argued that his proposal would "take politics out of our rule-making process so we can unite this party behind our nominee and defeat Hillary in November."

The rejection essentially punts the issue to the 112 delegates on the convention Rules Committee that meets later this week, meaning the big showdown will come Thursday and Friday, just as Trump is unveiling is vice presidential nominee.

"At this point in time it just seems to me we are a day before the beginning of the convention rules committee, I don't think we should be seen as a body to do anything that might abrogate the power of the convention rules committee," said Peter Feaman, a member of the RNC rules panel from Florida.

Anti-Trump delegates have to find at least 28 members of the 112-member convention rules panel to support their effort to free delegates to vote against Trump. Unruh has been touting that she has the votes needed, but an informal survey of Republicans behind the scenes at the RNC summer meeting Monday and Tuesday suggested they are not there yet.

The anti-Trump delegates, meanwhile, have worked hard to build out a campaign in the past four weeks and had set up shop just a few blocks from the convention center in downtown Cleveland by Monday.

Delegates Unbound -- the campaign operations arm of the group Free The Delegates -- had vote-counters set up in delegations for 30 states, as of Monday afternoon. Almost all were volunteers, with the group offering about $900 per whip to cover the cost of transportation to the convention in many cases.

But the strategy so far, which has relied heavily on email bombardment of rules members, has struggled to find traction among their target audience.

In one tense exchange emblematic of the lobbying challenges anti-Trump delegates have faced, Iowa RNC Committeeman Steve Scheffler confronted anti-Trump supporter A.J. Spiker outside the RNC rules panel meeting Tuesday.

Scheffler said Spiker was responsible for an ad that anti-Trump activist Steve Lonegan ran against him in Iowa.

"You ran that ad," Scheffler said to Spiker.

Spiker placed the blame on conservative talk show host and anti-Trump activist Steve Deace and quickly changed the subject to "prairie chickens and porn" -- two items being debated inside the Republican Party platform committee at the time.

When the convention begins in full next week, House Speaker Paul Ryan will hold the gavel. Speaking at a CNN town hall Tuesday night, Ryan said he was not going to put his thumb on the scale for either side in the delegate fight.

The speaker deflected a question from audience member Steve Lonegan, a New Jersey Republican who has been active in the effort to unbind the delegates.

"It is not my job as chairman of the convention to tell the delegates how to run their convention," Ryan said.