Such an exercise in nostalgia was necessary because Mr. Floyd, who since 2007 has served as local leader of the Teamsters union, couldn’t exactly take us around to the New York City of his present, since he, like many New Yorkers, decamped to Valley Stream, just over the Queens border on Long Island, when he couldn’t afford a home in the borough of his birth.

So he drove us to his boyhood home in Crown Heights, where a woman sitting on his former stoop asked first if he was a detective, then if he knew Sydney Poitier. We stopped by the deli where he worked after high school and where, at age 19, he picked up a copy of the union newspaper The Chief, and saw an ad that led to his joining his father as a member of the city’s public-hospital police force. And we visited the well-kept home his mother still keeps in Queens Village. On the walls were pictures of Mr. Floyd meeting Barack Obama and family portraits of Mr. Floyd with his father and two brothers, all in their dress blues.

Mr. Floyd has never run for, or served in, public office—and was elected head of the Teamsters in 2009 only after being appointed interim head when the scandal-scarred former president was pushed out in 2007. But he was inspired to seek the mayorality after watching some of the backlash earlier this year in Wisconsin and elsewhere to the rollback of collective-bargaining rights of public-sector workers. (Nationwide, the Teamsters are mostly long-haul truckers and construction workers, but in New York, Local 237 is a public-sector union of Housing Authority staff, school safety agents, hospital police and the like.)

“The mayor of New York City is the second most powerful position in this country. You know what the job of the governor of New York is? It’s to look in the papers every morning and see what the mayor of New York is doing,” Mr. Floyd said. “People will pay attention, if nothing else. I saw a man named Jimmy McMillan get national spotlight with one line: ‘The Rent Is too Damn High.’ And you know what? That is a silly message but people understood it. People heard it. We might laugh at the man but he got his point across.”

He continued, “People are running for office saying the most outlandish things. I said, ‘Greg, you’ve got a lot of things to say but no one wants to listen to you. What can you do? Well, you’ve got to run. You’ve got to run for something and at least try to get your message across.’”

That message? “That working men and women are in desperate need of help and if we don’t hear their cry there is going to be a revolution in this country. There will be bloodshed.”

Mr. Floyd compares the current economic situation in the country to Spider-Man, in which Peter Parker’s beloved Uncle Ben is murdered by a burglar whom Spidey had earlier failed to apprehend. “That is a lesson. You should have stopped the person and then your uncle would still be alive. Because you didn’t see the need to assist, it hurt you in the long run. So Wall Street does need to help somebody because I’m afraid there is going to be bloodshed in this country.”

So Mr. Floyd’s place in the field of 2013 mayoral contenders is clear, right? He’ll be the voice of working people, pulling the narrative to the left, defending the rights and perogatives of labor unions. Except the 2013 field is already filled with candidates tripping over themselves to be the candidate of the city’s powerful labor unions. Even Greg Floyd seems to think so.

Pressed on the other candidates in the race, Mr. Floyd mostly stuck to his opponents’ biographies.

“I think [Christine Quinn] is the front-runner. She has been a very good speaker of the City Council. She has been historic. First woman. I can see a lot of things she has done that are good.”

“[City Comptroller] John Liu is a very hard working individual. He has accomplished a lot. He is the first Asian-American elected official in the city and John has a bright future.

“Bill de Blasio is a very smart individual. Worked for the Clinton administration. Currently lives in Brooklyn.Another New Yorker.

“Scott Stringer. Former assemblyman. Borough of Manhattan president. Seems to be at every community meeting.

“Did I leave any out? Bill Thompson. Came very close to winning his last race. Was City Comptroller for eight years. His father is a judge. Grew up in Brooklyn. Now lives in Harlem.”

Another problem with Mr. Floyd as this campaign’s Ralph Nader is that he is something of an imperfect spokesman. This city is lousy with fire-breathing labor leaders, like Stuart Appelbaum of the retail workers union and Norman Seabrook of the Correctional Officers union, who are unafraid to throw bricks at the Bloomberg administration and bash the Wall Street oligarchs. The Teamsters, by contrast, have been a bit player, playing a peripheral role in the Working Families Party labor-backed electoral juggernaut and often siding with the Bloomberg administration and the building trades in contentious fights.

Moreover, his ideas on taxation aren’t exactly the kind of thing to set hearts racing in Zuccotti Park. When asked if he was concerned that going after the Wall Street wealthy would cause them to flee the city, he said, “I wouldn’t try to impose an exorbitant tax increase on the most wealthy. It would have to be a percentage on everybody. All eight million … You won’t drive business away if you increase taxes on everyone. If you increase taxes on just a certain segment it will drive people away.”

So what we have in the candidacy of Greg Floyd, then, is the leader of a union of public-sector workers at a time when the opinion of them is at its lowest ebb, a leader of a union whose name in the public mind is more resonant of a public menace than public safety. Further, Mr. Floyd told The Observer he plans on becoming the first mayoral candidate in recent memory to raise private funds but opt out of the city’s much heralded campaign finance laws, which impose strict limits on corporate giving and require disclosure of donors. And if that weren’t enough, he wants to campaign as the voice of the working class, but lives on Long Island, wants to impose broad-based tax increases on all New Yorkers, and speaks with conciliation toward the barons of Wall Street and admiration toward the Bloomberg administration.

“I find this whole thing very confusing,” said one political consultant who works closely with many city labor unions. “He’s not seen as particularly progressive. He doesn’t lead a huge union, and they don’t play a huge role.”

The candidacy of Mr. Floyd is so unlikely in fact that it has led to widespread speculation in political circles that he is being encouraged to run by Mr. Bloomberg. By this line of thinking, Mr. Floyd’s presence in the race is likely to steal union supporters away from Mr. de Blasio, peel minority voters away from Mr. Liu and Mr. Thompson, and keep other would-be candidates on the sidelines. All of which redounds to the benefit of Mr. Bloomberg’s all-but-appointed successor, Christine Quinn.

“I know this sounds conspiratorial, but it looks so obvious, it has to be a little true,” said one Democratic consultant. “This benefits Christine Quinn so clearly you have to wonder if supporters of hers or supporters of the mayor’s who are also supporters of hers are whispering in his ear telling him this is a good idea.”

Mr. Floyd declined to say who he has spoken with in anticipation of a run. A Bloomberg adviser said the rumors were untrue, as did Hank Sheinkopf, a Democratic consultant and lobbyist for the Teamsters, who made a case for Mr. Floyd.

“His message is that people who work for a living need a voice,” he said. “He is not somebody who gets checks from labor unions and then get to say they represent labor.”

Politics is never quite the dark arts that many assume it to be, and the likelihood of a massive pro-Quinn effort behind Mr. Floyd’s flirtations is small. But the effect of Mr. Floyd on the race remains the same: the longer he hangs around, the less likely another candidate who can slow the Quinn juggernaut—like Assemblyman Hakeem Jeffries or Bronx Borough President Ruben Diaz or even Mr. Thompson— will emerge,

And Mr. Floyd likely wouldn’t take much convincing to run. The benefits to his own position are huge, and include more name recognition for himself and his union and the possibility that the Teamsters become a central player in the city. His stated unwillingness to participate in the campaign finance system means that he will have free rein to bombard the city with advertising, which will increase his own profile.

Mr. Floyd opened a campaign account only last week, and at this point, an ultimate decision by him on whether or not to run remains several months off. He is aware that is candidacy is a longshot, but is determined to go ahead with it regardless. “Somebody else may be the winner, but we are going to set the agenda for the next mayor, that’s what we are going to do,” he said as the Navigator pulled away from his mother’s house in Queens. “I have a very good job. I am not looking to improve my standing in life. I’m looking to improve everybody else’s standing. I could sit down and be fine.”

dfreedlander@observer.com

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