There's always good old Time::Local and hand parsing (untested):

#!/usr/bin/perl

use Time::Local;
my $now_gmt = time;
my $then = "2004-01-14";
my ($ty,$tm,$td) = $then =~ /^(\d\d\d\d)-(\d\d)-(\d\d)$/;
my $then_gmt = timegm(0,0,0,$td,$tm-1,$ty);
my $diff_in_days = int(($now_gmt - $then_gmt) / 86400);
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