What happens when MS SQL runs out of identities?

You have a table, with an identity, that, due to the nature of your application, deletes and inserts many rows on a regular basis. It crossed your mind that at some time the key will grow to the largest integer and then what? You tell yourself that SQL will of course handle that for you , or at least it will never come up since 2,147,483,647 is a large number.

Well, today it happened to me.

[Microsoft][ODBC SQL Server Driver][SQL Server]Arithmetic overflow error converting IDENTITY to data type int.
[Microsoft][ODBC SQL Server Driver][SQL Server]Arithmetic overflow occured.

My "fix" was to reseed the table and change the datatype to bigint, I wonder how long until 9,223,372,036,854,775,807 rows have been inserted and then deleted?