Sieg Heil Herr Newt!!
The First Amendment says 1) the government is not allowed to stop people from challenging the government or from speaking about things, or the press from writing about things, AND, that the government can neither support one religion over others, or prevent people from practicing any particular religion. The overriding principle of this pivotal concept, which had its seed in Locke and in the Magna Carta, is that people need to be able to act their conscience (hence religion, which otherwise seems out of place), and to seek to sway others, including the government, to their side.
Herr Newt would like to take at least one idea out of the "marketplace." While violence as a means of political expression isn't generally socially acceptable, it's not all that rare, historically. Ask the Jews at Massada. Look at the Greek gods vs. the titans. Texas vs. Mexico. The Colonies and Britain?
The really scary bit here isn't the use of restricting speech to prevent terrorism, it's how such an action would affect all the other crazy-ass things that have happened since September 11, 2001. If they can monitor and restrict internet traffic, how long can they keep those records for? Who can they give them to? What would people not say if they thought they were always watched? What topics would be curtailed? With a fascist, pro-life, anti-speech, "trust me, don't ask questions" conservative regime in power, and a media that's already too scared to report on facts as they are for fear of persecution, what won't we hear?
Personally, I think that Gingrich's career in politics should be long dead. He should be unable to become representative of a city dump, much less a presidential candidate. Then again, this country elected the idiot son of an asshole twice, so he's probably the frontrunner at this point...