In the wake of the defeat of the so-called “millionaire tax” in Albany, lawmakers are turning to a new tax-the-rich scheme that they say has a better chance of passage.

Under the plan circulating around City Hall and Albany, general partners of a private equity or hedge fund would have to pay local business income taxes on their share of profits generated by investments.

The proposal follows a failed push by Assembly Democrats to raise the personal income taxes of people earning more than $1 million a year.

This year’s budget crunch and forecasts of declining tax revenues have intensified calls among elected officials for wealthy residents to bear more of the brunt of the down economy as a way to stave off budget cuts.

Critics of the tax plans argue that the wealthy in New York pay some of the highest taxes in the nation and that adding to their burden would only encourage them to move elsewhere, putting more stress on New York’s finances.

Governor Paterson, Mayor Bloomberg, and Senate Republicans opposed the broad-based increase, which was excluded from the enacted state budget.

The new version, developed by the Fiscal Policy Institute and other organized-labor activists, is a city tax, not a state tax, and would therefore have to be first approved by the City Council as a “home-rule” message and then voted on by the state Legislature. It is also smaller in scope. The plan’s crafters say it would raise about $200 million a year, compared to the $1.2 billion a year haul that was expected from the income tax hike.

The city currently taxes management fees that partners receive as their base compensation. The city’s 4% unincorporated business tax does not apply, however, to the “carried interest,” which typically amounts to about 20% of profits and is already subject to personal income taxes.

New York’s unincorporated business tax is imposed on incorporated businesses based or partly based in the city, including partnerships, limited liability companies, fiduciary associations, estates, and trusts. Most funds are structured as limited partnerships or LLCs.

Fiscal Policy Institute budget analysts say hedge fund managers would pay a 2% tax on income that becomes subject to the unincorporated business tax because of city and federal deductions and credits.

The size and targeted nature of the tax gives proponents hope that it will be more politically acceptable in Albany, where Mr. Paterson and Senate Republicans have resisted broad-based tax increases on personal or business income but have been more amenable to increases that have a more limited impact and can be billed as loophole closures.

Advocates of the tax hike said it would make it easier for city lawmakers to balance the city budget, which is due July 1, without having to rely on additional cuts to services or agencies.

“If the city sends a home-rule message and it expresses its desire to close this loophole and to tax private equity and hedge fund firms the same way they tax a freelancer or small firm, I don’t know why the Senate would be opposed to it,” a Democratic assemblyman of Queens, Rory Lancman, said. The primary force behind both proposals is the labor-financed Working Families Party, a third party that has been a source of political and financial support for lawmakers who are taking up the measure, including City Council members Robert Jackson of Manhattan and Hiram Monserrate of Queens,

“I would think that this has a decent chance,” the executive director of the Working Families Party, Daniel Cantor, said. “We’re talking about a few dozen people who are basically stealing a couple of hundred million dollars from the city.”

City lawmakers and labor organizers are unveiling the plan with a rally today on the steps of City Hall. In 2005 at least 34 of the 51 members of the New York City Council had run on the Working Families Party line.

Carried interest earned by hedge fund and private equity managers had been the target of Congress last year. Efforts to increase federal taxes on that income failed, despite backing from both Senator Obama and Senator Clinton. Senator Schumer had pressed for any tax increase to apply not only to hedge funds and private equity funds but also to oil-and-gas partnerships and real estate partnerships with similar corporate structures.