A prominent Republican senator, Orrin G. Hatch, threw his weight behind the D.C. voting-rights bill yesterday in what supporters called a possible breakthrough in getting the legislation approved by that chamber.

Sen. Joseph I. Lieberman (I-Conn.), who introduced the bill yesterday with Hatch (Utah), said both men would start lining up support in the Senate. Lieberman, chairman of the key Homeland Security and Governmental Affairs Committee, pledged to hold a hearing on the legislation this month.

"I . . . am certain [Hatch's] co-sponsorship will lead to the breakthrough we've been searching for to bring an end to the 200-year disenfranchisement of District residents," Lieberman said.

The legislation is a political compromise that would pair a new House seat for the heavily Democratic District with another seat for Republican-leaning Utah. Hatch's state just missed getting a fourth representative after the last census.

A similar voting-rights bill passed the Democratic-controlled House two weeks ago. But the fight is expected to be tougher in the Senate, where Democrats hold a razor-thin margin. The Republican Senate leader has strongly opposed the measure, raising the specter of a filibuster.

Even if the legislation passes the Senate, the White House has threatened a veto.

Supporters of the bill were elated by the leading role assumed by Hatch, a 30-year Senate veteran who is widely respected in Congress, particularly among Republicans. As a former Judiciary Committee chairman, Hatch could be an influential counterweight to those who have called the bill unconstitutional, advocates said.

"It's very, very important," said Rep. Thomas M. Davis III (R-Va.), who co-sponsored the House bill with D.C. Del. Eleanor Holmes Norton (D). "You need a leading Republican face" to get the bill passed.

Senate Minority Leader Mitch McConnell (R-Ky.) reiterated his opposition to the measure, however. Asked whether Hatch's move would change Republican minds, McConnell said: "Well, it doesn't change the Constitution. And the Constitution's really quite clear on it."

Critics of the D.C. vote legislation say it violates the constitutional requirement that House members come from states. The bill's supporters argue that the Constitution gives Congress sweeping powers over the District, which would allow for giving it full representation in the House. Prominent legal experts disagree over which side is right.

Hatch said he had been persuaded by arguments that Congress treats the District as a state in many ways. "These arguments lead me to believe it is only fair that we proceed with this legislation," he said.

The Lieberman-Hatch bill differs from the House version in several ways. The Senate legislation would redraw Utah's electoral map to add the extra House seat, instead of temporarily establishing an "at-large" seat chosen statewide. Hatch had strongly opposed the "at-large" provision as unconstitutional.

In addition, the Senate bill takes effect with the 2008 elections, rather than with the current Congress. That provision addressed concerns that Utah representatives would have to raise money to run in special elections in new districts.

If the Senate measure passes, the differences with the House legislation would have to be worked out in conference.

A recent Washington Post poll found that 61 percent of Americans think the District should have a full voting member in the House. The poll found that reaction is mixed to the idea of pairing a new D.C. seat with an extra seat for Utah.

Lieberman, a longtime champion of D.C. voting rights, had expected to shepherd the House bill through the Senate. But his plans were temporarily derailed last month when the Senate parliamentarian ruled that the measure should go to the Finance Committee because it contained a minor tweak of the tax code to pay for the new House seats.

To get around that issue, Lieberman and Hatch didn't include tax language in their legislation.

Lieberman and Hatch will have to get 60 votes to avoid a filibuster by Republicans, which would kill the bill. Lieberman predicted that most Democrats would support it. On the Republican side, Hatch said that Utah's junior senator, Robert F. Bennett (R), would co-sponsor the bill.

Asked whether he would talk to President Bush about approving the bill, Hatch said: "You bet."

Utah fell 856 people short of getting an extra House seat after the 2000 Census. The state protested that it had been shortchanged because the census didn't count thousands of Mormon missionaries working abroad.

The bill would give Utah the seat and an extra electoral vote until 2012, when redistricting takes place based on the 2010 Census. The legislation would permanently raise the number of House seats to 437.