SMS Backup will work with the new Google 2-step authenticator if you turn on plain-text authorization instead of the more complicated (but automatic) OAuth. You will need to create a per-app password.
The app runs in the background automatically, requires virtually no intervention.
If you want your stuff archived, this free solution is for you.
Rating: Get it
http://www.appbrain.com/app/sms-backup/com.zegoggles.smssync
