Well, if the OP already has the number of days in the future, it can be a lot simpler:

my $today_wday = (localtime)[6];
my $then_wday  = ($today_wday + $days_in_the_future) % 7;
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Update: But it sounds like he's just given a date string. If it's a simple MM-DD-YYYY, I'd suggest Time::Local+localtime, since it's core.

use Time::Local;

my $string      = "01-01-2015";
my ($m, $d, $y) = split /-/, $string;

my $epoch       = timelocal 0, 0, 0, $d, $m-1, $y-1900;
my $wday        = (localtime $epoch)[6];
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To do any of the other algorithms suggested, you'll need to parse out the day, month, year values anyway.. If this is a problem, you will need a beefier date module like Date::Calc.