Parties don't always take opposite sides of each issue. Frequently, they try to take the higher ground by claiming they do "more" ...
Wouldn't it be wonderful for both parties to compete as to who opposes draconian garbage like SOPA/PIPA more?
Democrats could push for European-style subsidy of production. Republicans could push for letting the market work - advertising, product placement, etc are all that's needed. Both programs can agree on eliminating copyright for entertainment works.
I can see the Republicans trying to strongly dissociate themselves from SOPA, but I give it approximately 0% chance that they're going to recant the DMCA or Sonny Bono Copyright Extension Act, or even loosen their position on the DMCA moderately to the extent of supporting more exemptions to the anti-circumvention clause.