I'm not sure what you meant by "credit card closeout", but here's an idea. If you're concerned about the balance being charged and due the next billing cycle if you make the payment later in the day of final payment there's a chance it want appear on the current statement. Sometimes it takes two days to show up. This isn't guaranteed, but possible. If it shows up on the next bill having some interest is better than risking losing out on a cruise, plus your deposit.
If you're at your limit and you can't go over assuming you have good credit open another credit card and use it.
As previously stated call and ask for an increase if this is an issue.
I would not call Celebrity and try and get an extension. Even if they said yes, how can you trust them?
The bottom line is if you want to go on the cruise get creative. Figure out how to make this work.