You would get the following error..straight from the beast himself apparently
Msg 666, Level 16, State 2, Line 1
The maximum system-generated unique value for a duplicate group was exceeded for index with partition ID 72057594039173120. Dropping and re-creating the index may resolve this; otherwise, use another clustering key.
I will be using DBCC PAGE and DBCC IND in this blog post, if you want to learn how to use these yourself, take a look at How to use DBCC PAGE
One horror story along these lines I’ve heard was a system where the developers would insert every new row with a clustered index value of 0 and then subsequently update the row to set the column to its correct value. This does not decrement the uniquifier, though, so eventually you hit the limit even if there are only a relatively small number of 0-valued rows.