If this bill passes, the first thing that is going to go up is Anti-SOPA public DNS servers... Just like using 4.2.2.2 as your DNS, there will be public DNS servers that either omit the information from the SOPA blacklists, or they will actively use it as a reference of what's currently blocked so they know what to push through to the direct IP of the source manually.
That and I'd also be willing to bet Google and Mozilla (probably not Microsoft) will build anti-SOPA plugins directly into their browsers making them automatically recognize when you try to access a page that has been blacklisted - and redirect you to the source IP address instead using said public DNS servers.
Sure, this will cause a bit of a headache for a while, but let's not forget, we live in a time where if you want it bad enough, no government can keep you out.