If neither side strongly supports or opposes something but lobbyists strongly support it then expect it to pass John Doe.
The best way to stop SOPA would ironically be the democrats strongly coming out in support of the bill, which would make the house suddenly refuse to even vote on SOPA, and would cause the bill to be filibustered in the senate. Why, because republicans have to oppose anything Obama/democrats are for.
Republicans strongly supporting SOPA would also likely kill it. The house would pass it, and Reid would refuse to even bring it to a vote in the Senate, or would bring it to a vote knowing that it'll lose just to show republicans that it can't pass the senate.
If you doubt me then look at the payroll taxcut fight going on right now. Republicans always support tax cuts, except when Obama & democrats support it, like the payroll tax cut being discussed.
The pharmacy lobbyists know this as well, there was part of Obama's healthcare law (I forget what part) that big pharma wanted removed from the bill that a lot of democrats had opposed when the healthcare law was written. Big pharma lobbyists told Republicans not to go on a public rampage demonizing that provision and blaming it on Obama, republicans demonized it and Obama for signing it into law anyway, and dozens of democrats who had previously voiced opposition to the provision voted against repealing the provision when the House voted on it months ago, and Reid refused to even hold a vote on it.
So the moral of the story? If we want to kill SOPA we just need to convince one political party to strongly support SOPA. The other party will reflexively strongly oppose SOPA and block it from ever becoming law.