Copy 8 Million Records
Your operation will most likely be a logged operation as you're performing an insert.

Monitor the log file growth and you should see that's what is utilizing your remaining disk space.

Consider inserting using a minimally logged approach, these include:


BULK INSERT
INSERT...SELECT
MERGE with Trace Flag 610


I have also found an insert to a column with an identity specification will also cause logging to occur.

Links: 
http://blogs.msdn.com//b/sqlserverstorageengine/archive/2008/02/05/bulk-logging-optimizations-minimal-logging.aspx
http://www.sqlmag.com/article/tsql3/minimally-logged-inserts

Also: I would recommend inserting into a heap and then apply your indexes unless your data has been pre-sorted in the source database.

Consider defining the identity value in your source database, select all the data into the destination and then apply the identity specification and set the seed.