I think that its quite possible that the Rats can lose some support and this would affect some of the more marginal races where the senate will be fought. The Rats are already in danger of losing unions over Alaska. Add to that the ban on free speech and they will take some hits in my opinion.
The GOP on the other hand are the lead group for gettting the AD ban turned down and won't likely suffer as much as the RATs.
I think Bush and is advisors saw this as part of the dynamics for the after affects of his signature.