The anticipation of a de Blasio 2020 campaign is not much higher outside New York City. The mayor polled at 1 percent in two polls in March, two-thirds of what he would need to qualify for the first Democratic debate in June. But Mr. de Blasio polls at zero percent in many polls, and his name is not listed in others.

Taylor Blair, who was until recently the president of the Iowa State University College Democrats, was among those who received a polling call from Mr. de Blasio’s potential campaign in May.

He was asked 25 specific questions seeking to find which parts of the mayor’s record might engender support. Beyond the paid poll, Mr. Blair said, he has heard little discussion of Mr. de Blasio.

“No one is out here talking like, ‘Oh, I hope Bill de Blasio runs. He’d be my guy,’” he said.

Even the advisers who helped Mr. de Blasio win City Hall are not backing a presidential run.

Mike Casca, who formerly worked on Senator Bernie Sanders’s 2016 presidential campaign and in his office, was hired to be Mr. de Blasio’s communications director. After volunteering for several months for Fairness PAC, the political action committee that the mayor is using to fund his trips, Mr. Casca left his City Hall job to work directly for the PAC last month — only to leave that job last week.

A person familiar with discussions around the PAC said Mr. Casca had originally told Mr. de Blasio that he would help get the committee off the ground, but he came to the conclusion that the mayor should not run for president and told him that he would not stay around for a possible campaign.

Emma Wolfe, Mr. de Blasio’s chief of staff, is not involved in his exploratory efforts. Neither are most of the political consultants Mr. de Blasio named as agents of the city, advisers whose advice was so valued that the mayor argued his communications with them should be shielded from public view.