you probably want to check out date::manip.
Failing that, I'd try mucking with the following POSIX compliant time formats.

%U     week of year, Sunday as first day of week     - 01 to 53
%W     week of year, Monday as first day of week     - 01 to 53
[download]

and do something like :

get today's date.
get today's week of year. (WOY)
while the current day's WOY = today's WOY
    retrieve and print articles
[download]

yeah.
why bother with epoch time when POSIX and Date::Manip are there to let you work on what you need to do, rather than figuring out mundane and error prone epoch time calculation?

---

Oh, a code sample? OK :

use POSIX;
use strict;

#
#   get epoch time and format to Week of Year.
#
my $today = time;
my $current = strftime("%W",localtime($today));




#
#   Is today a sunday?
#
if (strftime("%w",localtime ($today))==0) {
    #
    #   Yes, retrieve last week's news.
    #
    print "getting last week's news.\n";
} else {
    #
    #   Nope, look for each day this week.
    #
    my $check = $current;
    while ($check==$current) {  
        #
        #   while WOYs are equal, retrieve that day's news.
        #
        print scalar(localtime($today)) , " is this week. Retrieving a
+rticles.\n";
        #
        #   back a day.
        #
        $today -=86400;
        $check = strftime("%W",localtime($today));
    }
}
[download]