While mayoral hopefuls have gone to great lengths to keep the West Side stadium proposal in the headlines, Mayor Bloomberg seems to expect that by the time voters go to the polls in November the issue will be exhausted.

Yesterday, as the speaker of the City Council, Gifford Miller, was out with poster-board charts talking about the stadium’s “hidden costs,” Mr. Bloomberg shrugged off the recent barrage of negative stadium publicity, saying he had no plans to roll out a new advertising campaign to set the record straight.

“I think before the campaign gets going in earnest, hopefully the stadium will be approved and will happen and we won’t have the problem of doing that,” Mr. Bloomberg told reporters at City Hall.

He said he would not “worry about the silliness of advertising” or putting “everything in a context of an election.”

With the International Olympic Committee scheduled to select a host city for the 2012 Games this July, the mayor will have four months to recover from the political fallout of its decision. If New York does win the bid, the stadium could become an asset for the mayor, some analysts said.

“By the time people focus on the mayor’s race for real in the fall, this is going to be a comparatively minor issue,” a professor at Columbia University’s School of International and Public Affairs, Steven Cohen, said. “The real issue is whether or not his opponents make the case and it sticks in people’s minds that Mayor Bloomberg is an out-of-touch guy.”

Mr. Cohen, who said he thinks Mr. Bloomberg has done a good job, predicted that by early fall, in time for the Democratic and Republican primaries, the administration will be able to shift the public dialogue back to its accomplishments, such as reduced crime and the improved economy.

“Most people don’t pay a lot of attention to these things until the fall,” Mr. Cohen said. “The polls are certainly moving around a lot, but people have not made up their minds on who to support and they are not going to until later.”

Yesterday, however, Mr. Miller was riding the momentum he and the other Democrats have created to tear down Mr. Bloomberg’s push for the New York Sports and Convention Center. That facility, to be built on a platform over the Hudson rail yards, would serve as a home to the New York Jets, an expansion of the neighboring Jacob K. Javits Convention Center, and the bedrock of the city’s Olympic bid.

The council plans to pass legislation intended to block the mayor from diverting money from the operating budget to pay the city’s portion of the stadium costs. Mr. Miller and company were out on 34th Street and 11th Avenue in front of the site yesterday, calling on the mayor to come clean on the city’s costs.

Mr. Miller, one of four Democrats seeking the party’s nomination to challenge the mayor, said city taxpayers would be on the hook for at least $151 million more than the $300 million Mr. Bloomberg has agreed would be the city’s contribution.

That money, the council speaker said, includes $30 million for a pedestrian tunnel, $55 million for a platform over West Street, and $66 million for a “game porch,” or elevated plaza, that would be attached to the 75,000-seat domed arena.

A spokeswoman for the Jets, Marissa Shorenstein, rebutted that. The Jets, she said, have already committed to paying for the game porch and are also paying for other public infrastructure, such as a pedestrian bridge at 33rd Street and part of another at 39th Street.

A spokesman for the mayor, Jennifer Falk, said that the deck over West Street would be needed only if the city wins the Olympic bid, and that if it is built it will be paid for by NYC2012. She also said the city would not be on the hook for the $30 million pedestrian tunnel. That would be paid for by the Javits Center or another entity.

Council Member Christine Quinn, who represents the West Side district and has been outspoken in her opposition to the project, said New Yorkers should not have to “sweeten the pot” for the Jets with their tax money.

At their 10:30 news conference, Mr. Miller, Ms. Quinn, Betsy Gotbaum, who is the city’s public advocate, and a group of about a dozen anti-stadium activists were confronted by a rowdy prostadium group of union workers. The protesters, mostly iron and metal workers, initially tried to stymie the event with loud chants of “Stadium Yes! Gifford No!” Mr. Miller, however, quickly cut a deal. In exchange for a few minutes of quiet, he offered the metal podium that he stands behind at news conferences, so that the group could address reporters with a response. It worked – but the union was still adamant in its position.

A representative from Local 46, Terrance Moore, said the Jets were the “first people in 40 years to build anything on this piece of property.” Plus, he said, the stadium increases the city’s chance of winning the Olympics, the ultimate job creator.

Meanwhile, the city comptroller, William Thompson Jr., said yesterday that his office would conduct an audit of the city’s Economic Development Corp. to examine the PILOT payments it receives from businesses. That is the money the mayor has proposed using to pay the city’s $300 million share of the stadium.

Mr. Thompson, a Democrat, testified in front of a City Council committee during the first day of budget hearings that he had “serious concerns” about the “transparency” and “accountability” of the way the payments tracked. The goal is to complete the audit within three months.