If you have access to phpMyAdmin then it’s possible.
phpList records in table username_usermessage which campaigns each user has been sent, and also if they were opened. When you requeue a campaign the system looks at this table and will send the campaign to any users for whom there is no entry for that campaign in the table. In normal usage this is a way to send a campaign to people who signed up since the campaign in question was first sent.
If you edit the table to delete the records for that campaign then on requeing the campaign will be sent again. The SQL to use would be something like
DELETE FROM username_usermessage WHERE messageid = n
obviously substituting actual values for the bits in italics.
@oatmeal You can use the Campaigns plugin to resend a campaign to specific subscribers. It does what @Cornwell described for the usermessage table, but also can remove bounce records.
On the Manage Plugins page follow the “Find Plugins” link.