It will be available in a few different ways, including what you mentioned (entering a URL and seeing the "conversational graph").
We're open to more suggestions -- thanks for the feedback!
For now, I'm stuck with "view this on Digg", "view this on Reddit", etc... which will work well for users of those specific networks, but not for someone such as myself who wants to get a wider view of discussions across all networks.
I have to ask, if most comments don't extend to Digg, Reddit, etc, where do they come from? The blog post itself?
In addition to Digg, Reddit and Hacker News, we're looking at other blogs as well as FriendFeed and Twitter.
My app aims to be a kick-off service that allows users to jump to whatever web service they need to use at that moment... without me having to do any other work than pointing them to the correct URL... so I don't prefer the onus to be on me to create this functionality with your API :)
My own personal needs aside, I think the web-wide discussion of a URL is a pretty impressive and useful feature for general consumption... I really hope you include it.