Can you keep on using the website while waiting? In this case you shouldn't black out the entire screen; rather block the actionable area which is the login form or at the very least the button itself. Since changing the text inputs won't have any effect, to me it would seem logic to block the entire screen (or even replace it with a whole different "trying to login..." screen.
Is the login button the start of your flow? E.g. Facebook app for which you must first log on. In this case you may block the entire window or again replace the form with a "trying to login..." screen. Again, only the button would not provide any benefit as changing something here is not useful.
Idea behind it: show only what you need, when you need it; limit confusion and ambiguity.