Chairman Murkowski is apparently waiting on the activity in the House before making any decisions. The bill has bipartisan support, with 11 senators cosponsoring it. The Jeffords bill includes a strong RPS, a PBT, emission controls, and strong net metering and consumer information disclosure provisions. The Union of Concerned Scientists strongly supports the Jeffords Bill. Together with other national organizations such as US Public Interest Research Group, National Resource Defense Council, and the Alliance to Save Energy, UCS has rallied behind the Jeffords Bill in the Senate.
All senators make decisions based, at least in part, on what they hear from their constituents.
While many senators are generally supportive of the provisions in the Jeffords Bill, they are not likely to cosponsor the legislation unless you take the step of communicating with them.