Mr. de Blasio, after all, has mostly failed in polls to win the support of white voters, even many Democrats. He is struggling to contain a surging homeless population. He clashes fruitlessly and often with Gov. Andrew M. Cuomo, a fellow Democrat.
His administration is mired in a series of overlapping fund-raising investigations, including some by the United States attorney for the Southern District of New York, Preet Bharara, that could result in indictments of Mr. de Blasio or top officials in the coming weeks. The mayor was interviewed by federal prosecutors for four hours on Friday.
It might seem enough fodder for any challenger. But defeating an incumbent in New York City is no easy task; a one-term mayor has been ousted only twice in the last 50 years: Abraham D. Beame by Edward I. Koch in 1977, and David N. Dinkins by Rudolph W. Giuliani in 1993.
There is another side of the ledger to consider, political observers said, that has so far warded off serious contenders in the Democratic primary — often the deciding contest in a city where registered Democrats outnumber Republicans six to one.
Crime has remained low on Mr. de Blasio’s watch, even as he has moved to overhaul police practices despised by Democratic voters. The economy is growing. The administration has pushed through new programs to address the needs of the less fortunate, who are also Mr. de Blasio’s base of support, like universal prekindergarten and a push to build affordable housing. He champions the rights of transgender people, immigrants and low-wage earners. He finds broad support among blacks and majority approval from Hispanics.
“He’s in this sweet spot of being progressive enough to satisfy the progressives, but not so far to the left that people think he’s an unrealistic leader,” said Christina Greer, a professor of political science at Fordham University. As for quality of life in the city, she added, “Things are either status quo as they were under Bloomberg, or not as bad as people said they would be under de Blasio.”
The election of President Trump has also been a boon for the mayor, who staked out a position as a vocal opponent of the new administration early on.
Another factor in the mayor’s favor is that most of the logical Democratic contenders, like Scott M. Stringer, the city comptroller, would have to leave their office to run for mayor. The safer route would suggest waiting until 2021, when Mr. de Blasio would have to leave office because of term limits.
Nonetheless, Mr. Stringer, who has been flirting with a run for months, has publicly clashed with Mr. de Blasio on policy matters such as homelessness, child welfare and policing. The city’s public advocate, Letitia A. James, is still mulling a run, though Representative Hakeem Jeffries of Brooklyn, once considered a possible top contender, has all but ruled one out.
Others have been quietly considering jumping in, including Christine C. Quinn, the former City Council speaker who lost to Mr. de Blasio in 2013, and Daniel R. Garodnick, a Manhattan city councilman who cannot seek re-election this year because of term limits.
What has held nearly every Democrat back from making a firm decision is the uncertainty surrounding the federal investigations, they or their aides said. An indictment of one or several members of the de Blasio administration could be enough for some of those waiting in the wings. Criminal charges against Mr. de Blasio would cause a flood of entrants.
“If I had to bet, Stringer still stays out because that’s who he is,” Mr. Tusk said. “Quinn’s a tougher call. Garodnick only runs if no one else does and he has a clear shot.”
The longer a decision by prosecutors takes, the more difficult it will be for a challenger to mount an effective campaign before the September primary and the November general election. So far, only Mr. de Blasio’s main Republican opponent, Paul J. Massey Jr., a real estate sales executive, has rivaled him in fund-raising, though Mr. Massey has also spent money faster than he has taken it in from donors.
“It’s not so much that the mayor is operating from a position of tremendous strength,” said David S. Birdsell, dean of the Baruch College School of Public Affairs. “It’s that he doesn’t have exploitable weaknesses of the sort that would allow a challenger to easily mount a credible campaign.”
The mayor’s critics on the right contend that City Hall is awash in corruption and mismanagement. On the left, he is attacked as acting too slowly or not aggressively enough on housing and policing. Such criticism has prompted an advocate of criminal justice reform, Robert Gangi, to declare a long-shot bid for mayor.
Even rising homelessness, if it does not affect quality of life or crime in the city, may not have an effect on his chances. “It is a tragedy,” Mr. Birdsell said of the human impact of homelessness, “but the homeless by and large don’t vote.”
Those who dislike Mr. de Blasio also point to his occasional lateness, his penchant for traveling from Gracie Mansion to a Park Slope gym many weekday mornings, and his supercilious demeanor during news conferences — traits that the handful of declared candidates have seized on.
“The mayor needs to be replaced because he’s distracted, doesn’t work hard and is mired in conflicts of interest,” said Sal F. Albanese, a Democrat who has run for mayor several times.
“I cannot stand by and let a corrupt, noncaring, lazy mayor continue,” said Bo Dietl, a retired police detective who wanted to run as a Democrat but did not file the paperwork in time. (“I will run as an independent,” he said.)
State Senator Tony Avella, a Democrat from Queens, said he was running because “ineffective management” had made the city “a place that is nearly impossible to afford to live or retire in.”
Mr. Massey, who secured endorsement of the Independence Party, said he was running “because there is a failure of leadership and sound judgment” at City Hall. He is joined in the Republican field by the Rev. Michel J. Faulkner, a pastor and former New York Jets defensive lineman, who has been waging a campaign based on serving “the neediest New Yorkers.” (John A. Catsimatidis, the billionaire supermarket magnate and radio host, is also said to be considering another run.)
But failures of personality, style and management do not equate to the sorts of crises that have shaken incumbent mayors from their powerful pedestals in New York City history.
“It is very possible that he could win even though his approval ratings are low,” Hank Sheinkopf, a veteran political consultant, said of the mayor. Mr. Sheinkopf has met with eight potential challengers to Mr. de Blasio about working on their campaigns. He has yet to decide if he will.
The mayor began mounting his campaign last year, shifting a key adviser, Phil Walzak, to the re-election effort in October. He has moved to lock up endorsements from 11 unions so far, including those representing teachers and municipal workers, and from the Working Families Party, which has helped many Democratic candidates in their ground game.
He has broadened his base of donors, employing a small-dollar fund-raising operation used by Senator Bernie Sanders in his presidential campaign. Mr. de Blasio has $2.2 million in campaign cash on hand, far more than everyone but Mr. Stringer, who has $1.7 million in the bank.
“There is no complacency here,” Mr. Walzak said.
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