“I think it’s important to remember that threats are more than someone saying I’m going to come to your house and I’m going to hurt you... Insulting someone’s appearance, insulting someone’s religion, or their race, you know, all of that to me constitutes a threat and I think we can make changes to how we control that dialogue on the internet without threatening our First Amendment rights.”So, you want a broad definition for "threat," going beyond what you called "violent bullying." (I'm going to guess that "violent bullying" refers to words of violence — like "kill" and "rape" — directed at a particular individual and not restricted to a context where the target is going to need to worry that the the violence will occur.) You want "threat" to cover insults of all kinds, including the banal remarks about how somebody looks and the politically important critiques of religion. Then you want to avoid "threatening our First Amendment rights." But if I accept your meaning of the word "threat," then you are already threatening our First Amendment rights.
This word game works both ways.
I don't know if Dunham was thinking in terms of the actual law, but she did say "First Amendment." "First Amendment" understood narrowly only refers to what the government might do to us. Since Twitter is a private company, no control of the dialogue by Twitter can threaten First Amendment rights, if we stick to the narrow idea. Therefore, we can even adopt Dunham's definition of "threat" and say there can never be a threat to First Amendment rights, no matter how restrictive of speech Twitter becomes, because our oppressor is a private corporation.
"First Amendment" is already too narrow a term for the threat under discussion. We need to say "freedom of speech." This is a topic I've discussed at length elsewhere on this blog — notably here — so I'll stop this post now.
ADDED: Here I am in March 2011 fighting hard for my position that we need to care about what private enterprises can do to our freedom of speech: