It seems a natural part of the web that the conversation carries on across a number of channels. I'd guess that changing behaviour would be quite a challenge, so I wonder if there's a technological solution.
What if your blog showed you (as the author) a list of relevant tweets in the sidebar, with a button that copied the tweet into your site's comment-stream?
There's some tech problems to solve here: how does the site calculate which tweets are relevant, in order to suggest them to the author? What steps are needed to copy the tweet into the comment stream for a particular post?
Hmm, that gives me an idea for my blog...