Joe Lieberman's proposal

Joe Lieberman has recently proposed that if a U.S. citizen should commit acts of terrorism against the U.S., that person should have citizenship removed from them. This is not the strange part, the strange part is that Nancy Pelosi and John Boehner both agree it's not a good idea. You know, for someone who couldn't swallow a public option or let younger people buy into medicaid, this is certainly a strange move, because the State Department makes the list on what groups are considered foreign terrorists. Any one in these groups qualifies. Ok, I see one big loophole already: what about the ones who start homemade terrorist groups? Next, how does this fit under the constitution? I don't think it can be done, nor do I believe it should even be attempted. What do you think?