The Washington Post reports that the upcoming (probably on Tuesday) vote over a bill giving Washington, D.C. a full Congressional representative could be tight:

The vote could be a cliffhanger. Almost all of the Senate's 51 Democrats and independents back the bill, as do at least five Republican members.

The vote needs 60 votes to overcome a filibuster. Who's in play?

The bill's supporters are focusing on a small group of senators who are publicly uncommitted, including Arlen Specter (R-Pa.), Richard G. Lugar (R-Ind.), Robert C. Byrd (D-W.Va.) and Sam Brownback (R-Kan).

Many opponents of the bill claim that it is unconstitutional--that Congress cannot legislate a seat to the District of Columbia, which is not a state. They cite Article I, Section 2 of the Constitution to support this claim (e.a.):

The House of Representatives shall be composed of Members chosen every second Year by the People of the several States

Some argue that Congress still has the power to grant DC a seat even if it isn't an official state.
Sen. Warner (R-VA) has announced that he will not support this measure--though he is interested in a Constitutional amendment to grant DC a full representative in the House. Other opponents of this bill might be interested in a similar amendment.
A similar bill has already passed the House, and the White House has threatened to veto this bill.