Backup very large table I have to update certain values of a large table (for the sake of a presumed example, it is called 'Resource' and it is over 5M rows) and thus I have to make a backup before performing the changes. We do not have enough DB free space in order to store the full backed-up table.

Which is the best way? Is there a way to do this by blocks? I mean something like: backing up the first 100K rows from the original table, updating those 100K rows in the original table, deleting those 100K rows from the backed-up table, backing up the following 100K rows from the original table, and proceeding analogously. Is this feasible?
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.