The Whitney Museum of American Art is expected to get final city approval today for its downtown expansion plan, just as the economic turmoil has made the museum’s $680 million fund-raising goal more daunting than ever.

The City Council is set to vote today to approve the Whitney’s plan to construct an 185,000-square-foot building, designed by Renzo Piano, on Gansevoort Street next to the High Line. The design has already been approved by the council’s Land Use Committee; the city Planning Commission; the president of Manhattan, Scott Stringer, and the local community board.

“This is the last stop,” the Whitney’s spokesman, Jeffrey Levine, said of today’s council vote. “Everything has gone well so far, so we’re feeling positive.”

If the approval process this time around has gone relatively smoothly — much more so than for the Whitney’s previous plan to expand its uptown facility — the same will probably not be true for the capital campaign, which Mr. Levine described as currently in its “silent phase.” The $680 million goal, which includes $435 million for construction, would be a large hurdle at any time, but particularly so when members of New York’s financial community are feeling under siege.

“Obviously the financial world has changed in the last week, but we still remain confident that this is a great project for the city,” Mr. Levine said. “We haven’t changed our commitment to the project.”

Even before the last week’s economic news, the Whitney needed to find some new big donors. The museum’s chairman emeritus, Leonard Lauder, 75, said in March that his art foundation would donate $131 million to the Whitney, the largest donation in the museum’s history. But that money will go toward shoring up the endowment, not construction of the new building. Mr. Lauder even made it a condition of his gift that the Whitney not sell its 1966 Marcel Breuer building, on Madison Avenue at 75th Street, for an extended period of time.

What the Whitney needs now is to find another Stephen Schwarzman or David Koch — a billionaire eager to put his name on the façade of a major city cultural institution. Mr. Levine said that not all of the money has to be raised before the museum breaks ground, which is expected to happen in late spring 2009. The new building is expected to open in late 2012.