Here you see Sen . Joe Lieberman suggesting that if any American citizens "choose to affiliate themselves with foreign terrorist organizations" we should be able to revoke their citizenship. Since then he has co-sponsored a bill to this effect. If passed, it would apply to native as well as naturalized Americans. Come to think of it, that would include me.
Consider first what he is not saying: He is not saying that if you are found guilty in a court of law of conspiring with a terrorist organization, then (as part of your punishment, perhaps) you might be stripped of your citizenship. No. He is saying if you are accused of being affiliated with a terrorist organization, you can be stripped of your citizenship and then (maybe!) a court will figure out whether you are guilty of anything.
Lieberman talks as if the officials making the accusing somehow just know whether you are "affiliated" with terrorist or not. The problem is that procedures and standards of proof make all the difference in the world. In his bill the accusation would be made, not by a judge or jury, but by the Department of State. Once you have lost your citizenship, you might be moving into a legal category where the standards of proof and procedural protections are a lot lower that they were before. According to the above-linked article, if you are captured overseas (while on vacation pershaps?) you can end up detained in a place like Gitmo, with the same rights that its inmates have.
According to law profs quoted in the same article, the bill is written so broadly that "affiliating" yourself could include writing a check to Hamas or Hezbollah, or helping them to do something that happens to be perfectly legal (such as making a presentation to the UN).
The very first thought I had when I first heard of the 9/11 attacks was to wonder what the US reaction would be. All I was fairly sure of was that it would be an over-reaction. Years later, the over-reactions continue.