It is not for lack of trying.

Since the new year, Mr. de Blasio has aimed announcements on health care for undocumented New Yorkers and a new plan for paid vacation at television and news media audiences far beyond the five boroughs. His proposals are a model, he said in television interviews on “The View” and on MSNBC. He promised a series of trips around the country to “preach the gospel” of liberal governance on everything from education to police reform.

The efforts follow a fund-raising push by Mr. de Blasio last year via a national political action committee, Fairness PAC, that raised $469,000 since he started it in July. He doled out modest sums through the committee for candidates in contested races for governor and Congress, and $25,000 each to the state Democratic parties in Iowa and South Carolina — key presidential primary states.

“He spent some Q.T. there,” said Mr. Benjamin, referring to the quality time Mr. de Blasio spent in South Carolina in September. Mr. de Blasio dined with the chairman of the state Democratic Party, Trav Robertson, during the visit. He later contributed money to the party, as have other potential candidates, including Mr. Bloomberg and Mr. Garcetti.

Mr. de Blasio continued his push on Thursday, energetically bounding onto the stage at the mayors’ conference for his first address outside New York since his pledge to spread the good word.

But as a player in the 2020 conversation, Mr. de Blasio does not yet register even among his fellow mayors, where he holds clout as the leader of the nation’s largest city, nor among many strategists.