It’s the same as when the democrats got republicans to help them get cloture in the senate. Boehner may indeed get it passed, but having to do that with the help of democrats weakens him as a leader. And that task should be made as difficult as possible, while at the same time exposing those that want to have it both ways.
Yes, I know all about switching votes between cloture and actual bill so the reps can lie to us about their vote. But trying to kill bills through the rules vote is less effective since, per the article, you have Dem yeas anyway there. At least on the final vote you should have a bunch of Dem nos, which means that many fewer Repubs you need to also vote no.
Obviously, yes, we want as many noes as we can get, and as often. I just think, given politician math, it’s much easier to get the noes on the main vote instead of the rule/cloture where everyone and their mother usually votes yes.