Backup very large table
Two thoughts come to mind.


If you are concerned that this update may not properly affect the table the way you think, have you thought about putting the update inside a transaction.  
You could do the update, query the data, and if it all looks okay, Commit the Transaction.  If it fails, you could perform a Rollback.


Alternative

You may want to look at the BCP utility to extract the table to a flat file outside of the SQL Server.

Presumably, you could store the contents of the table in a location where you aren't under as much storage pressure.  If the update process fails, you could attempt to restore the contents back into your table.