A bill giving the District its first full seat in Congress cleared the House yesterday, marking the city's biggest legislative victory in its quest for voting rights in nearly three decades.

Democrats on the House floor burst into applause, and Speaker Nancy Pelosi (D-Calif.) grabbed the arms of the District's nonvoting delegate, Eleanor Holmes Norton, as the 241 to 177 vote was announced.

"There was nothing but joy in the chamber this afternoon, because we knew we had given this bill the kind of send-off that can get it through the Senate," Norton (D) said later.

But the bill faces considerable obstacles. Democrats don't appear to have enough votes in the Senate to avoid a filibuster, and the White House has threatened a veto. If the measure becomes law, it probably will be challenged in court.

Sen. Joseph I. Lieberman (I-Conn.) vowed to bring the legislation to the Senate "as quickly as possible." Aides said he would seek a vote on the bill by the Homeland Security and Government Affairs Committee, which he chairs, in the next few months.

The legislation, sponsored by Norton and Rep. Thomas M. Davis III (R-Va.), would add two seats to the House: one for the overwhelmingly Democratic District and another for the next state in line to pick up a representative, Republican-leaning Utah.

Although the bill was fashioned as a political compromise, only 22 Republicans supported it, including one from Utah. All but six Democrats present voted for it.

Several Republicans contended that the bill violated the constitutional requirement that House representatives come from states.

"The Constitution is clear. Let's follow it or amend it," said Rep. Louie Gohmert (R-Tex.), who brandished a poster with constitutional quotes during the debate.

The bill's supporters argued that the District deserves full House representation because its residents pay taxes and serve in the U.S. military. They said a D.C. seat could be created under constitutional provisions giving Congress sweeping powers over the District.

Democrats steered the bill through final House passage a month after it was temporarily derailed by Republicans who tried to attach language overturning the District's strict anti-gun laws.

This time, Democrats broke the voting rights measure into two bills written so narrowly that Republicans couldn't change them much under House rules. One would add the two representatives to the House, and the other would make a small change in the tax code to pay for the legislation.