The bill will be in reapple if it violates the First Amendment of the Constitution. Then they'll make adjustments to it and try and pass it again..Frankly until I see any official news report regarding the bill going to Congress I don't believe it and it's just another rumor..even if it comes from Firefox..
The first amendment covers the ability to have no limit of direct speech, freedom of expression, creativity and religious beliefs of the american people. This includes from the government. The first 10 "laws" are called the bill of rights. These 10 rights can not be infringed upon. The only reason you can violate an american's bill of rights is to protect the national security, prevent the collapsing of democracy(aka Marshall Law/Defcon 1), and if that person is deemed a threat to the country (again National Security).
This would indeed be a direct violation of the bill of rights as the internet is only a median of freedom of express and creativity and such browsing of the internet is no direct and/or immediate threat to national security. If you are engaging in "terrorist activities" on the internet, you are already breaching the law in multiple ways, regardless if you intended to act on such actions or not.
This will not be passed, if it was the United States Supreme Court will shoot it down before its even know it was passed as it violates the constitutional rights of Americans.
If this is passed and not shot down. There will be some serious shit going down. I will be moving to Italy should this occur.
(( I am a Government/History Education major FYI this is how I know all this useless crap ))