Se3ssions raised the issue earlier in the day yesterday during debate. The motion was made by Tester in an attempt to get around the objection. Under current Senate rules, 1 Senator can stall everything under the unanimous consent rule (If all 100 vote yes, not debate, the bill passes). Sessions knew that his caucus would not break ranks to vote for a D, so Tester's only route was to try and siphon off a few votes from moderate R's who felt that this bill did not violate the Budget Control Act, and since it was a fee not a tax, they should move it forward. Only one Republican, Olympia Snowe, voted for the motion. All else voted against, or were absent.
This brings up the other rule that the Senate has instituted: The Fillibuster rule. It requires a vote of 60 senators to move any legislation forward. In a bitterly divided congress, reaching 60 votes is next to impossible, especially if the caucus' get their heels dug in.
Some D's did not vote because they have ties to the enviros who opposed the bill (like Boxer, who at least had the stones to vote no.) The vote ended up coming down as 50-34. Several from each party sat it out because they knew 1.) It couldn't get 60 without them, 2.) They didn't want the heat of voting on it.
As for the Tester/Thune Amendment, here's the NRA's action alert on it from June 15th, 2012:
http://www.nraila.org/legislation/f...-week.aspx?s="Tester-Thune+amendment"&st=&ps=