Test if a Post is the Last of the Day

Howdy,
I’m trying to figure out a way to test if a post is the last post of a particular day. Take a look at my blog at http://polaricecap.net and you’ll see that each of my posts has a paragraph tag containing the post date off to the left of the title. I’d like the paragraph containing the date to show only if it is the last (or latest) post of the day, so that the a particular day’s date only shows once. Another example: Gruber’s blog does this at http://daringfireball.net/

Basically, I’m looking for this:

IF there is no later post timestamp OR if the next timestamp’s date is different, add a class name LAST-DAY to post’s container.

Any ideas?