Ok, that helps. if you look at your themes index.php, that date on every post is being called with the following:
<?php the_time('F jS, Y') ?>
the first step toward what you want is removing that bit of code from your index.php
The second bit (putting back one date for each day) is done by adding this:
<?php the_date('','<h2>','</h2>'); ?>
Putting the above line immediately below the following line:
<?php while (have_posts()) : the_post(); ?>
should achive what you want.
you will get one big date enclosed with h2 tags that you can style to your liking in your css.