The once-robust Oversight and Investigations Committee, which Ms. Quinn’s predecessor used to highlight differences with the Mayor, has been relatively quiet since she took office. And Ms. Quinn hasn’t exactly jumped to grab headlines, even when openings have presented themselves.

(Remember what she said recently when Mr. Bloomberg insisted on enforcing parking regulations after a snowstorm, or his administration’s rerouting of school buses that left 6-year-olds out in the cold? No?)

Such chumminess between a Mayor and a Speaker who aspires to be Mayor is not without precedent. When the City Council’s first Speaker, Peter Vallone Sr., ran for Mayor in 2001, he came up with the following unofficial slogan: “I only have to walk 65 feet across City Hall to keep things going.”

“They were nowhere near City Hall or the passage of the law,” Mr. Vallone said in a recent interview, explaining why he thought his literal proximity to power was an advantage over his Mayoral opponents. “What I tried to do is say, ‘I’m here—where are you? And I can take over right from where he is.’

“I think the more you keep your differences private, the better the city is,” he continued. “So whatever disagreements they have should be cordial and private until it becomes a matter of public concern. And I think she’s doing that very well.”

Despite (or perhaps because of) his amicable relationship with then-Mayor Rudy Giuliani, Mr. Vallone finished third in the 2001 Democratic Mayoral primary.

The next Council Speaker, Gifford Miller, tried a different tack, building a Mayoral platform by taking every occasion to differentiate himself from Mr. Bloomberg. But his campaign in 2005, like Mr. Vallone’s four years earlier, was a bust.

So far, Ms. Quinn has appeared to lean more toward Mr. Vallone’s 65-foot strategy than to Mr. Miller’s more confrontational model.

But will things turn out any better for her than they did for Mr. Vallone?

As in 2001, the field in 2009 is going to be crowded, and is likely to include a City Comptroller, a Public Advocate and a Bronx borough president, among others. And as in 2001—and 2005, for that matter—it is turning out to be a difficult task for the Speaker to remain in good standing with the other members of the City Council without harming her ability to appeal to the voting public.

Mr. Vallone said that Ms. Quinn’s seemingly amicable relationship with the Mayor was “a terrific step in the right direction.”

He seemed hesitant to offer odds on Ms. Quinn’s potential candidacy. “Her chances are as good as anybody else’s now, because it much too early,” he said.

But Mr. Vallone did offer her some advice: “Just strive to do the right thing, and the public will understand that in the long run—even if it’s not popular at the time.”