Some Rubio backers in the early states are voicing concern about whether Mr. Rubio is leaving voters there with the impression that he does not need them to win. And some of Mr. Rubio’s own aides are now arguing privately that they should do more to push back against the belief that he is running an indifferent campaign before it becomes too widespread.

“The campaign efforts for Marco Rubio in Iowa can very easily be perceived as wanting to place in the top three in the caucus and not necessarily to win,” said Kenney Linhart, a pastor in Des Moines who is supporting the Rubio campaign. Regardless of how serious Mr. Rubio is about trying to win the state, Mr. Linhart added, the belief that he is not is harmful: “Perception is as powerful as intent or will.”

Indeed, Mr. Rubio’s light footprint in Iowa has been the talk of the state’s political community for months. He was unable to hire a local operative to run his campaign there, and instead brought on an Arkansas-based Republican strategist, Clint Reed, in September to oversee his Iowa campaign. And Mr. Rubio is relying on 31-year-old Eric Teetsel, who lives in Kansas, to handle outreach to social conservatives and evangelicals — rankling some Iowans used to a more neighborly outreach.