Escalate to your manager. Go back and tell him what you just told us, but phrase it as, "How do you want me to spend my time as a resource?" If, as you say, they intend for the code to be supported indefinitely, you can lean on the unsupportability of the current code as a reason for him to give you the time to do it right.

Of course, then you have to deliver. Especially if you haven't before gotten to do a project, this is a great opportunity to show you are sensitive to the needs of the business as well a worthy of greater responsibility.

(Gaack ... I hate it when I fall into businessspeak)