WASHINGTON — Senator Charles E. Schumer of New York, the Senate’s third-ranking Democrat, threw cold water on Tuesday on one emerging approach for striking a bipartisan deficit-reduction deal — an overhaul of the tax code that lowers top income tax rates but raises more revenue. Mr. Schumer’s position complicates efforts to seal a deal before January, when the “fiscal cliff” of tax increases and automatic spending cuts goes into effect.

In a speech to the National Press Club, Mr. Schumer branded the idea of a tax code overhaul that could simultaneously lower the top rates, bring in more revenue and protect middle-class taxpayers from increases as “little more than happy talk.”

Instead, he said that the top two income tax rates should be frozen around 36 percent and 39.6 percent, which are levels from the Clinton era, and that any additional revenue generated by closing loopholes and curtailing or eliminating tax deductions and credits should be devoted to deficit reduction.

“It is an alluring prospect to cut taxes on the wealthiest people and somehow still reduce the deficit, but you can’t have your cake and eat it too,” said Mr. Schumer, a member of the tax-writing Finance Committee. “The reality is, any path forward on tax reform that promised to cut rates will end up either failing to reduce the deficit or failing to protect the middle class from a net tax increase.”