A day after it was disclosed that President Bush is predicting Senator Clinton will defeat Senator Obama to win the Democratic presidential nomination, Mr. Obama is swooping onto Mrs. Clinton’s turf to raise money, announce a new endorsement, and, on Thursday, address supporters at a rally in Washington Square Park that could be the largest public event he’s held in the city.

It’s all part of a big New York push that appears to be designed to tap the city’s deep pockets, raise the candidate’s profile, and show he isn’t going to back away from the city even though Mrs. Clinton maintains a deep lead here in the polls.

Tonight, Mr. Obama is attending a “Barack on Broadway” fund-raiser at the New Amsterdam Theater on 42nd Street, hosted by the president of Disney Theatrical Productions, Thomas Schumacher, the president of the Broadway theater company Jujamcyn, Rocco Landesman, and Broadway musical producers Scott Sanders, Roger Berlind, and Margo Lions.

This morning, he is scheduled to announce what his campaign is calling a “key endorsement” at the Omni Berkshire Place hotel on East 52nd Street at Madison Avenue.

In a sign that Mrs. Clinton is not going to let such a move go unchallenged, her campaign issued an alert hours after Mr. Obama’s campaign announced the endorsement, saying the New York senator is scheduled to receive a “major national endorsement” of her own in Washington today.

Senator Bayh, a Democrat of Indiana, will endorse Mrs. Clinton today, the Politico reported yesterday, citing Democratic sources Last week, the Service Employe,es International Union said it had three finalists for endorsement: Mrs. Clinton, Mr. Obama, and John Edwards, the former senator of North Carolina.

The Reverend Al Sharpton, whom some political observers speculated could have been Mr. Obama’s “key endorsement,” said yesterday he has not made up his mind.”I’m not leaning any way right now,” he said, adding that much of his decision about who to support will “be based on the candidate that stands for the strongest social justice agenda.”

Mr. Bush’s prediction about Mrs. Clinton’s primary victory was first reported by the Drudge Report yesterday in a story about a book, “Evangelical President,” scheduled for release today. Mr. Bush also predicts in the book that a Republican candidate would defeat Mrs. Clinton for the presidency, according to the report.

A Siena New York poll released last week found that among Democratic primary voters, Mrs. Clinton would score 42% in a primary match, with Mr. Obama coming in second with 17% of the vote.

Despite these figures, Mr. Obama’s campaign is forging ahead with plans to raise his profile and support base in New York through Thursday’s rally and various press and broadcast appearances.

On Thursday, he is appearing on an ABC daytime talk show, “the View,” and taping an interview with a former supermodel who is now a talk show host, Tyra Banks, which will be broadcast next week, a spokeswoman for the Obama campaign, Jennifer Psaki, said.

Ms. Psaki would not predict how many people would attend the free event in Washington Square Park, but the campaign is trying to attract a crowd, having mounted a video on YouTube and on the campaign Web site in which Mr. Obama looks into the camera and invites people to attend the rally.

“I’m coming to New York City on September 27 and I want you to join me, to join this campaign, to join something historic, to be part of changing our politics,” he says in the video. “This campaign is a growing movement and now is the time to come together.”

Mr. Obama has been successful at attracting large crowds on the campaign trail: More than 20,000 people flocked to see him in Atlanta, and 20,000 came out in Austin, Texas, according to published reports. In Iowa City, Iowa, he attracted 10,000 people.

A spokesman for the police department, Michael Wysokowski, said he did not know the number of police officers that would be dispatched to the rally, because plans for the event were not available yesterday. A spokesman for the Parks Department, Warner Johnston, said he did not immediately know how many people would attend the rally.

Washington Square Park is considered the heart of Greenwich Village and has a rich history of political action and activism, the executive director of the Greenwich Village Society for Historic Preservation, Andrew Berman, said. For many, the park is associated with the anti-war protests of the 1960s and 1970s and counter-culture protests.”It’s certainly a place one would associate with making statements in a left-leaning vein,” Mr. Berman said.

A chairwoman of the grassroots political organization, Brooklyn for Barack, Jacqueline Esposito, said her organization has been trying for some time to convince Mr. Obama to hold a free rally in New York.

“The crowds that Barack Obama generates — it’s just unprecedented. Young people, older people, the people who come out for this candidate are just incredible,” she said. “It’s sort of that mentality: If you build it, they will come.”