The District of Columbia House Voting Rights Act cleared a major hurdle Tuesday when the Senate voted to begin debate on the bill, but Republicans can still set up a few obstacles to delay or prevent its final passage.

The bill, which would give the District its first-ever full House seat, passed a cloture vote 62-34, ensuring that the Senate will debate the bill and making its eventual passage likely.

Celebrating the Senate action, D.C. Del. Eleanor Holmes Norton (D) said the “critical vote” took years of perseverance to obtain.

“This was a long and hard-fought battle,” she said at a press conference. “We have already shown by today’s vote and today’s fight that we are ready” for any future obstacles.

As the District’s only Delegate, Norton can vote in committee but not on the House floor. The voting rights bill would give the Democratic-heavy city a voting Representative while also granting the Republican-leaning Utah the extra seat it narrowly missed getting after the 2000 Census.

Therefore, House Membership would expand to 437.

The bill last hit the Senate floor in 2007, when it fell just three votes short of the 60 needed to block a filibuster. That same vote succeeded on Tuesday, thanks to a more Democratic Senate.

A companion bill also is moving quickly through the House, where it is expected to easily pass. The Judiciary Committee plans to mark up the bill today, and House Majority Leader Steny Hoyer (D-Md.) said Tuesday that he hopes to bring it to the House floor by next week.

But as the debate unfolds on the Senate floor over the next few days, Republicans are expected to introduce amendments that could delay the legislation’s passage.

GOP Senators also have told Democrats that they may either require a second cloture vote to end debate or ask for a 60-vote margin on final passage, according to Democratic aides.

That could be problematic, since a few of the 62 Senators who voted for cloture Tuesday said they did so because they thought debate was important — not because they necessarily support the bill.

That includes two Republicans who didn’t vote for the same procedural motion in 2007: Sens. Lisa Murkowski (Alaska) and Thad Cochran (Miss.).

Cochran hasn’t said whether he will vote for the bill’s passage, releasing a statement declaring only that he decided “the Senate should have the opportunity to debate the options.”

Murkowski, however, made it clear Tuesday that she doesn’t support the bill.

“The people of the District of Columbia have expressed quite clearly that they want to have this debate. We should have this debate,” she said, but added: “I’ll be voting against this bill.”

At a press conference Tuesday, Senate Majority Leader Harry Reid (D-Nev.) said he hoped to have a final vote by the end of the week, but he also acknowledged the possibility of a stumbling block with Republican-offered amendments.

“I don’t know what amendments will be offered by Republicans, but I hope they will be constructive,” he said. “We know that a vast majority don’t want this bill passed. That’s too bad.”

Republicans chiefly object to the bill on constitutional grounds, arguing that the District can’t have a voting Representative because it isn’t a state.

But the bill’s supporters argue that the Constitution’s District Clause, which gives Congress authority over the city, trumps the Composition Clause, which states that Members of the House are elected by the “people of the several states.”

The bill does have some bipartisan support. Six of the eight Republicans who voted for the cloture motion Tuesday have been steadfast supporters of the bill: Sens. Arlen Specter (Pa.), Orrin Hatch (Utah), Susan Collins (Maine), Olympia Snowe (Maine), Dick Lugar (Ind.) and George Voinovich (Ohio).

Democrats are also on board, with only two definite exceptions: Sens. Max Baucus (Mont.) and Robert Byrd (W.Va.), both of whom voted against the cloture vote in 2007 and again on Tuesday.

But it’s freshman Sen. Kay Hagan’s (D-N.C.) uncertainty about the bill that has caused anxiety among voting rights advocates.

Hagan is one of the 62 Senators who voted to begin debate, but she said Tuesday afternoon she is still “reviewing the bill.”

But she also said she would vote in support of a second cloture vote, if Republicans require it to end debate on the bill and begin a final vote. A second cloture vote could derail the bill, if enough Senators voted for the cloture vote just to have a debate and decide not to support the bill.

Hagan’s uncertainty in recent days surprised voting rights advocates, who had all but assumed that new Democratic freshmen would support their cause.

Supporters were also a little thrown when Utah Sen. Bob Bennett (R) voted against the cloture vote Tuesday, despite his support in 2007.

“We were counting him as a yes and he ended up as a no,” said Ilir Zherka, executive director of the advocacy group DC Vote. “I think it goes back to what I’ve said before: In Congress and especially the Senate, it is unpredictable.”

D.C. Mayor Adrian Fenty said he would be working to gain the support of uncertain Senators such as Hagan over the next few days, taking his lead from Reid and the bill’s co-sponsor Sen. Joe Lieberman (ID-Conn.).

But Fenty and other voting rights advocates mostly focused Tuesday on celebrating the cloture victory.

“Today is a breakthrough in the full franchise of the people of the District of Columbia,” Fenty said at a press conference. “I was here two years ago on the floor of the Senate. … We fell three votes short that day, but I think everyone knew that the spirit of the people of the District of Columbia is not to be denied.”

If the House and Senate versions pass each chamber as is, the bill would have to go to a conference committee in order to iron out some differences — mainly, the fact that the Senate bill gives Utah a new district, while the House gives the state an at-large seat.

John Stanton contributed to this report.