List nodes within a date range
I'm assuming you know how to filter the view to get the nodes based on the date and date + 6, but are having troubles grouping them together on output by date. 

I see you are using D7, but to do this in D6, you would add the date field twice in the view and override one of these with a template to output just the day in question and group on that now simplified field.

A good article on that is http://drupal.org/node/388140 which shows you how to do it by month; to do it by day just change the date function to include it as well. 

I would imagine D7 is very similar, and that this helps out.