In the confidential files of at least two Democratic mayoral campaigns, aides have compiled a series of derogatory remarks by Mayor Michael R. Bloomberg about building a stadium in Queens for the 2012 Olympic Games.
Mr. Bloomberg spoke those words before he embraced that very same idea of a Queens stadium on Sunday, in hopes of salvaging the city's bid for the Olympics after state legislators scuttled his plan for a stadium in Manhattan.
For strategists in those camps, the question is whether to turn the mayor's words against him. Could they call Mr. Bloomberg a flip-flopper, a label that harmed John Kerry's presidential candidacy in 2004? Or should they hold off, not to appear negative three weeks before the Olympic committee selects a city?
"When the mayor flip-flops to the correct position, to a position we've sought for months, it becomes very hard to criticize him," said Brian Hardwick, the campaign manager for Gifford Miller, the City Council speaker. "But we need to make clear that the stadium reflects the mayor's wrong priorities for the city."
Scoring points against the mayor, be it about the stadium or other issues, has proved a challenge for the four Democratic candidates, analysts say. As Mr. Bloomberg seeks a second term, he has pulled the rug from under his rivals time and again: matching calls for affordable housing with a huge rezoning project along the Brooklyn waterfront; answering criticism of his schools policy with news of higher student test scores; countering attacks on a West Side stadium by ultimately embracing the Queens stadium.
Now the Democrats want to drive home a message to voters by depicting the mayor as out of step and two-faced in his quest for the Olympics. Yet they are going up against a mayor who is projecting a can-do image, or at least a can-try one, while they are seen on the sidelines.
"At the end of the day the stadium is a land-use issue, and it doesn't galvanize voters except in Manhattan," said George Arzt, a political communications consultant who is not working for any candidate. "The challenge is, can you fit the stadium into a theme of attack on Bloomberg? The negative theme in many polls is Bloomberg as an uncaring mayor, but the stadium doesn't connect on that level."
Attacking the mayor in a way that sticks has also proved difficult because Mr. Bloomberg is not an easy political target, neither especially divisive nor bumbling nor controversial, political analysts say. To unseat a sitting mayor, it is crucial for a Democrat to make voters see the incumbent as a failure, and Mr. Bloomberg's relatively smooth image has forced them to try to make the most of muddled issues like stadium plans.
"If Bloomberg inspired only love or hate in voters, you could write off the folks who love him and go after those who hate him," said Lee M. Miringoff, the director of the Marist Institute for Public Opinion. "Bloomberg is in the 'doing O.K.' category, and 'doing O.K.' is much harder to lay a glove on. He's doing O.K. on the Olympics because he's willing to try a Plan B."
The strategic bind for the Democrats became clear yesterday in an interview with one of them, Representative Anthony D. Weiner.
Mr. Weiner said Mr. Bloomberg had flip-flopped on the Queens stadium and said voters would judge the mayor critically if the Olympics bid was crushed because the alternate stadium was proposed so late in the Olympic bidding process.
Yet in the next breath, Mr. Weiner said he would send a letter today to Mr. Bloomberg proposing that he join the mayor on a trip to Africa this week to lobby International Olympic Committee officials before they select a host city next month.
Mr. Weiner, who was the first Democrat to propose an Olympic stadium in Queens, said that city politicians should present a united front to the committee but that did not mean Mr. Bloomberg should escape criticism for his handling of the bid.
"There's obviously a political element to the stadium, but there's also an element of coming together for New York," said Mr. Weiner, who represents parts of Brooklyn and Queens. "In three weeks, I hope the story is about Queens saving the Olympics. If it isn't, we'll be talking about the mayor's record of shifting positions on the stadium."
William T. Cunningham, a spokesman for the mayor's re-election campaign, dismissed Mr. Weiner's offer out of hand yesterday.
"After all of Weiner's snide comments about the mayor and the stadium, he now wants to ride on the airplane to Africa?" Mr. Cunningham said, laughing.
Aides to the two other Democratic candidates, Fernando Ferrer and C. Virginia Fields, say they believe that by Election Day voters will see the Olympic stadium as a sort of grand misadventure by a wealthy elitist who had no time left for the city's needs.
"We've seen the mayor go to Berlin to fight for the Olympics in a West Side stadium and to Africa to fight for the Queens stadium, but we haven't seen him in Albany fighting for school funding," said Jen Bluestein, a spokeswoman for Mr. Ferrer.
Joseph C. Mercurio, a consultant for Ms. Fields, predicted that painting the mayor as flip-flopping and misguided will eventually resonate with voters. But it may be a measure of the Democrats' task that the Bloomberg camp is certain these attacks will amount to only a din for voters.
"It's time for all these Democrats, who say they support the Olympics, to stand with the effort," Mr. Cunningham said. "Otherwise they look petty and snide and calculating. And guess what? They are."