It will certainly turn more against SOPA supporters.
I'm still finding so many that are unaware about SOPA and upon understanding that it's far-reaching attempt to control the Internet, they're not SOPA opponents. However, the older generation doesn't quite get it until I mention restricting Radio stations (They were familiar with the Pirate Radio in past).
People are lazy creatures. If something happens that inconveniences them in some way they will first hate the thing that caused the block (i.e. Facebook itself), but once they see that the initial target won't move they will hate the other party (i.e. SOPA)
Whereas removal of functionality will irk uncaring users and may turn them against the SOPA opposition.