Senate Democrats have yet to settle on a chairman of the Democratic Senatorial Campaign Committee.

Majority Leader Harry Reid, who was elected by his colleagues Tuesday to serve as Democratic leader in the 112th Congress, has struggled to find a taker for the DSCC job for the next cycle, when 23 incumbents are up for re-election. Unlike other leadership posts, the DSCC chairman is appointed by the Nevada Democrat.s

Potential candidates for the job include Sens. Tom Udall (N.M.) Mark Udall (Colo.) and Patty Murray (Wash.). Others, including Sens. Mark Warner (Va.), Al Franken (Minn.) and Michael Bennet (Colo.) turned down offers to replace Sen. Bob Menendez (N.J.) at the DSCC next year.

Meanwhile, Senate Democrats on Tuesday approved the rest of their leadership lineup for the 112th Congress. In addition to Reid, Majority Whip Dick Durbin (Ill.) and Conference Secretary Patty Murray will keep their posts for another term. But the rest of the leadership structure is poised to change.

Conference Vice Chairman Charles Schumer will take on an expanded role in the next Congress as co-chairman of the Democratic Policy Committee. The New York Democrat will have more control over legislative and communications strategy as head of the DPC, with Sen. Debbie Stabenow (Mich.) serving alongside him. The overhauled DPC will also house Reid’s own communications “war room” along with the policy portfolio, which was overseen by retiring Sen. Byron Dorgan (N.D.) over the past year. Sen. Mark Begich (Alaska), a Member of the 2008 class, will replace Stabenow as chairman of the Steering and Outreach Committee, which helps make committee assignments and leads outreach to independent interest groups.