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A consultant to Gov. Scott Walker of Wisconsin’s presidential campaign telephoned a Georgia-based Republican strategist last week to sound him out about working for Mr. Walker, a sign that he is considering staff changes at a moment when his campaign has been eclipsed by Donald J. Trump.

Mike McElwain, a partner at the media consulting firm that Mr. Walker has retained, called the strategist, Scott Rials, to ask whether he was available to move to Madison, Wis., to join the campaign.

“It was more of a, ‘would you be interested call,’” said Mr. Rials, who worked for Newt Gingrich and Rick Perry in the 2012 campaign. “It wasn’t clear what exactly the job was.” He stressed that no formal offer was presented.

That is often how such inquiries transpire in presidential politics, particularly after campaigns have started and officials are trying to quietly build or restructure their organization.

Mr. Rials, who lives with his family in the Atlanta area, said he told Mr. McElwain that he would not be able to relocate for the campaign.

Kirsten Kukowski, a spokeswoman for Mr. Walker, downplayed the call.

“A vendor for the campaign reached out to someone who pitched to work for us months ago,” Ms. Kukowski said. “There was no offer made at all in any way, shape or form.”

The backstage conversation took place the same week Mr. Walker saw his months-long lead in Iowa polls evaporate thanks to Mr. Trump’s surge there. After enjoying an early polling advantage in a state that neighbors his own, Mr. Walker, who made another trip to Iowa on Monday, fell 13 percentage points behind the bombastic reality TV star in a poll released by CNN.

It has been a jarring comedown for the campaign as it grapples with how to confront both the unpredictable Mr. Trump and Senator Ted Cruz of Texas, who is also showing strength with the conservative-dominated voters who tend to turn out for the Iowa caucuses.

“We got into the top-tier earlier than anybody expected,” said one adviser to Mr. Walker, adding of former Gov. Jeb Bush of Florida: “Our standing in Iowa is still going to be strong. The question is not whether Trump collapses but when, and where does that support go. Which is why Cruz may be the bigger threat to us than Jeb.”

Mr. Walker’s initial success in Iowa exceeded expectations of what he and his campaign thought possible early in the race, but now he is having to fulfill the expectations his initial strength there had created.

He has been running as more of a hard-line conservative than he was known for in Wisconsin, particularly on issues like immigration and same-sex marriage. Mr. Walker said on Monday on Fox News that his immigration views are “very similar” to the plan outlined on Sunday by Mr. Trump, which includes deporting illegal immigrants, making Mexico pay for a wall on the southern border and ending birthright citizenship. (Asked directly at the Iowa State Fair on Monday if he supported ending birthright citizenship, Mr. Walker said he did but would not say whether that meant he would deport the children of undocumented immigrants.)

Mr. Walker is sounding tougher rhetorical notes, too.

In an interview Monday on Glenn Beck’s radio show, Mr. Walker said he agreed with Mr. Beck’s assertion that Republican leaders like Senator Mitch McConnell of Kentucky, the majority leader, “are part of the problem” for the party.

“Yes. I hear it all the time and I share that sentiment,” Mr. Walker said. “We were told if Republicans got the majority in the United States Senate, there would be a bill on the president’s desk to repeal Obamacare. It is August. Where is that bill? Where was that vote?”

Mr. Walker also criticized Republican congressional leaders for not trying to block President Obama’s executive order of amnesty for millions of undocumented immigrants.

“This is where the frustration is,” Mr. Walker said. “This is why non-elected candidates are surging in the polls.”

Through his rise in Wisconsin politics, Mr. Walker has acted as his own chief strategist, devising his own TV commercials and press tactics. He had a small network of state-based advisers around him, but they have gone to work for his “super PAC” or have not been involved in the early months of his presidential run.

Mr. Walker’s campaign is led by Rick Wiley, a seasoned operative who first got to know the governor when serving as executive director of the Wisconsin Republican Party while Mr. Walker was the Milwaukee county executive.

Conspicuous thanks to a shaved head and robust goatee, Mr. Wiley has been a ubiquitous presence at Mr. Walker’s side, accompanying him on the road far more than is typical for most presidential campaign managers.

His constant travels with Mr. Walker have caught the attention of many in the small universe of political consultants, who believed that he was making the trips to ensure his voice was being heard by a candidate known to keep his own counsel.