I think the underlying issue is why you want to hide the URL. As everyone has noted, there is no way to solve the actual resolved URL. Once it is triggered, FireBug gives you everything you need to know.
However, is the purpose to prevent a user from re-using the URL? Perhaps you can generate one-time, session-relative URLs that can only be used in the given HTTP Session. If you cut/paste this URL to someone else, they would be unable to use it. You could also set it to expire if they tried to Refresh. This is done all the time.
Is the purpose to prevent the user from hacking your URL by providing a different query parameter? Well, you should be handling that on the server side anyways, checking if the user is authorized. Even before activating the link, the user can use a tool like FireBug to edit your client side code as much as they want. I've done this several times to live sites when they're not functioning the way I want :)
UPDATE: A HORRIBLE hack would be to drop an invisible Java Applet on the page. They can also trigger requests and interact with Javascript. Any logic could be included in the Applet code, which would be invisible to the user. This, however, introduces additional browser compatibility issues, etc, but can be done. I'm not sure if this would show up in Firebug. A user could still monitor outgoing traffic, but it might be less obvious. It would be better to make your server side more robust.