Yeah, they can try to re-frame it as a vote against "corporate fat-cats", etc., but "voted against the 1st Amendment" is not only true, it's simple to understand and "catchy".
Oh, and even if said vulnerable Senator votes against the bill, the opposing candidate can always run pretty much the same ad, using Reid as the target and pointing out that voting for “Senator X” is the same as voting for Reid. Even GOP incumbents will be able to use that approach.
“Let’s put it this way: would you like the be a vulnerable Senator, facing a difficult-enough already re-election campaign, and have to choose between alienating your crucial base or being hit with the label of “voted against the 1st Amendment”.”
I don’t see it that way at all. I think concern about individual liberty and constitutional rights is so far down the list of the Dim base that you would have to do a lot of digging to even get to it. They are concerned about abortion, minimum wage, open borders, and homosexual/lesbian/trans-whatever agendas.