Try updating your Expect module. I was able to reproduce your problem with the following code using Expect.pm 1.11, the default on Debian Woody. The problem went away with 1.15.

#!/usr/bin/perl -w
use strict;

use Expect; # version 1.11!

my $ssh = Expect->new('ssh tilrman@localhost');
$ssh->debug(1);
$ssh->expect(60, q{tilrman@localhost's password:});
$ssh->send("********\n");
$ssh->expect(60, '$');
$ssh->send("exit\n");
$ssh->close();
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Strangely enough, if you add a single semicolon -- apparently causing Perl to hand off to the shell -- 1.11 works too:

my $ssh = Expect->new('ssh tilrman@localhost;');
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