Using INTO in a simple or bulk logged recovery model uses minimal logging, so depending on how much data your moving you shouldnt see that much of a transaction log jump.
The amount of logging for SELECT...INTO depends on the recovery model in effect for the database. Under the simple recovery model or bulk-logged recovery model, bulk operations are minimally logged. With minimal logging, using the SELECT… INTO statement can be more efficient than creating a table and then populating the table with an INSERT statement. For more information
How much data are we talking about moving?