Senate Majority Leader Harry M. Reid hopes to bring the D.C. voting-rights bill to the floor for a crucial vote the week of Sept. 17, his spokesman said yesterday.

Supporters celebrated the announcement, saying they think the measure, which would give the District a full seat in the U.S. House, has enough backing to pass. Sen. Joseph I. Lieberman (I-Conn.), a co-sponsor of the bill, indicated that he thought it could survive a filibuster attempt.

"The senator is pleased that the vote has apparently been scheduled and is confident he will have the 60 votes necessary to move this measure through the Senate," said Lieberman's spokeswoman, Leslie Phillips.

The Senate minority leader, Mitch McConnell (R-Ky.), opposes the bill, saying it violates the Constitution by granting a full seat in the House to a non-state.

The bill, designed as a political compromise, would add two seats to the House. One would be for the staunchly Democratic District; the other would go to the next state in line to pick up a House seat -- currently Utah, which leans Republican.

It passed the House in April.

Lieberman, co-sponsor Sen. Orrin G. Hatch (R-Utah) and other supporters have been trying to persuade senators to let the bill go to an up-or-down vote. They would need a supermajority of 60 votes to proceed if Republicans threaten a filibuster.

Reid thought the legislation did not have that level of support before Congress adjourned for the August break. But he included the measure on a list of bills he wants considered in the next few weeks. And yesterday, Reid "indicated there will be a vote on D.C. voting rights the week of Sept. 17," said his spokesman, Jim Manley.

The District's nonvoting delegate, Eleanor Holmes Norton (D), said she is pleased that Reid "continues to make D.C. voting rights a priority in the face of a backlog of bills."

Ilir Zherka, director of the advocacy group D.C. Vote, called Reid's announcement "great news."

Senate passage would be a milestone in the city's decades-long efforts to secure representation in Congress. But the bill would face other hurdles.

President Bush's aides have urged him to veto the measure if it reaches his desk. And if it becomes law, it will probably face a quick court challenge. Legal scholars are divided on whether the bill is constitutional.

The bill has won strong support from Democrats. Last week, former Arkansas governor Mike Huckabee became the first Republican presidential aspirant to endorse it. Norton, who sponsored the D.C. vote bill in the House with Rep. Thomas M. Davis III (R-Va.), thanked Huckabee yesterday.

"Your support could prove especially helpful as we seek to make the point that this is not a country where voting rights bills are filibustered any more," she wrote.