Updated 12:43 p.m.

The District of Columbia House Voting Rights Act overcame a major hurdle Tuesday, passing a Senate cloture vote by 62-34.

The vote allows the Senate to begin debate on the bill, which is expected to start Wednesday or Thursday.

The bill is almost certainly assured passage now, although Republicans 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.

The bill would give the Democratic-heavy District a voting Representative in the House and Republican-leaning Utah an extra seat that it just barely missed adding in the 2000 census.

It would also increase the number of Members in the House of Representatives from 435 to 437.

The vote split roughly along partisan lines — with Democrats voting for it and Republicans against — with a few exceptions.

Only two Democrats voted against cloture, West Virginia’s Robert Byrd and Max Baucus of Montana.

Most notably, Utah Sen. Bob Bennett (R) voted against the procedural motion, despite the fact that it would give his state an early extra seat and that he voted for it in 2007.

Though Bennett supports the extra seat for Utah, he said his support in the past “was contingent upon resolving constitutional questions surrounding the bill.

“After further review, I have been convinced that this legislation exceeds the authority that the Constitution vests in Congress, and there is no viable amendment I could offer to remedy this and other constitutional concerns,” he said in a statement. “I am confident that Utah will receive its fourth congressional seat when the 2010 census results are announced.”

Only eight Republicans voted for cloture, but that included two new GOP votes since the bill was last on the Senate floor in 2007: Sens. Thad Cochran (Miss.) and Lisa Murkowski (Alaska).

Three Senators were absent and did not vote: Edward Kennedy (D-Mass.), Jim DeMint (R-S.C.) and Tom Harkin (D-Iowa).

In 2007, the bill came just three votes short of the 60 needed to stop a filibuster. That failure essentially doomed its chances for the 110th Congress, and it never made it back to the floor.

But the mood was markedly different this time around, with voting rights advocates more certain of victory because of a Senate that now has 58 Democrats, plus a few sympathetic Republicans.

On Tuesday, Senators from both sides of the aisle took to the floor to argue for and against the bill, rehashing arguments on the constitutionality of the bill.

Supporters say the District Clause of the Constitution gives Congress the ability to hand the city a Representative; opponents say the Composition Clause specifies that only states can have a voting Representative.

The bill is also moving quickly through the House, where it is expected to easily pass. The Judiciary Committee will hold a mark-up Wednesday, and Majority Leader Steny Hoyer (D-Md.) has pledged to quickly bring it to the House floor.

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