Sen. Patty Murray was buttonholed on the Senate floor Monday night by Democratic colleagues, many facing re-election in 2012, who urged her to lead Democratic Senatorial Campaign Committee next year.

According to a Democratic Senate aide, a host of Members approached the Washington state lawmaker Monday night during a floor vote to encourage her to take over the DSCC next year. Among those seen talking to Murray on the floor were Sens. Claire McCaskill (Mo.), Amy Klobuchar (Minn.), Sherrod Brown (Ohio) and Dianne Feinstein (Calif.). Outgoing DSCC Chairman Bob Menendez (N.J.), Washington counterpart Sen. Maria Cantwell and longtime colleague Sen. Chris Dodd (Conn.) also cornered Murray, who has emerged as the top choice to lead the DSCC.‬

The charm offensive, which came just as Members returned to Washington following the Thanksgiving break, is the latest in a mounting campaign to persuade Murray to head the Democrats’ Senatorial committee next year when 23 incumbents face re-election in a host of battleground states. Murray, who won a close re-election battle earlier this month, has also been approached by Majority Leader Harry Reid (D-Nev.) and White House deputy chief of staff and former Senate staffer Jim Messina.

A senior Democratic source said Murray, who has been “seriously considering” taking the job, would likely decide this week. However, she plans to continue talking with a number of colleagues this week before doing so. 

Democratic aides also said there has been talk of Murray moving to take over the Veterans’ Affairs chairmanship, considering Chairman Daniel Akaka (D-Hawaii) has the option to take the gavel at Indian Affairs next year. Akaka has been the subject of retirement rumors.

However, sources cautioned that even if Murray is able to take over Veterans’ Affairs, she is not necessarily angling to secure that job before deciding on whether to chair the DSCC. “She’ll decide this week [on the DSCC]. She’s not the type to play it out,” the senior Senate Democratic source said.

Murray’s willingness to take on the tough campaign job could put her in a better position to score the Veterans’ Affairs chairmanship, sources speculated, because no other Democrats are stepping up for the DSCC and the party would owe her some gratitude.

Murray has long coveted the Veterans’ Affairs gavel, and veterans issues have been one of her top concerns since arriving in the Senate in 1993.

The retirement of Indian Affairs Chairman Byron Dorgan (D-N.D.) gives Akaka a shot at the chairmanship of that panel. Taking Indian Affairs would position Akaka well to push his self-professed top priority: a bill to give native Hawaiians the same self-governing status as Native American tribes.

However, an Akaka spokesman said over the weekend that the Senator planned to stay atop Veterans’ Affairs. Reid spokesman Jim Manley further added Monday: “This is all idle speculation. No decisions have been made.”