Of course, that way you'll have to parse out the individual parts of the date (unless it will always be 2007-02-15):
$date_arr = explode('-', $date);
$my_time = mktime(0, 0, 0, $date_arr[1], $date_arr[2], $date_arr[0]);
$start_day = date('D', $my_time);
Using strtotime() would be more direct and flexible:
$start_day = date('D', strtotime($date));
And you can save some array storage also:
$start_month = date('M', strtotime($date));
Date and Time Functions