I'm honestly surprised Twitter never came up with their own blog commenting system, a la Facebook and Google+. Although, Facebook neglected theirs, so I assume there might not be a demand.
How would that work? Wouldn't it essentially be replying to a master tweet from the website (assuming the website auto-tweeted new submissions, something that many sites do now)?
It could just be a comment thread 1 level deep, a la the current Twitter Conversations implementation. The website can prompt the user to syndicate the Tweet to their stream. (This is also how Facebook Comments work.)
For comments, it would cut off the display on Twitter at 140 characters, with a link to view the full comment on the external site. This would also encourage site owners to adopt the system, as Twitter would push tons of traffic.