Well - that was my search query a couple of months back "how to auto publish from blogger to facebook page" - thought it was worth sharing!
So how do you do it?
Step 1 - Go to EDIT PAGE right under your page profile picture.
Step 2 - Scroll Down and look for NOTES
Step 3 - On Notes, Hit the EDIT Link
Step 4 - Scroll down to the bottom again and look for EDIT IMPORT SETTINGS
Step 5 - On the Next Page, Fill in your RSS Feed link in the space provided, check the authorization box and Hit it!
Now your posts on blogger will be Auto Published every time you put a new one! This will save you some extra minutes everyday + if you have already integrated the Facebook with Twitter, one more step will be saved!
Important: While auto publishing, to make sure that your feeds are published on the WALL for sure , on your EDIT PAGE > Under NOTES > Click 'APPLICATION SETTINGS and see that the 'Publish Content to my wall' is checked or not checked, as per what you desire.
Once you have integrated these settings all your earlier posts will get published all at once on the wall. So make sure you have either disabled the 'Publish to Wall' first or instead go and manually remove the feeds on the wall that you don't want to flood the page with.
Wordpress users can also follow same steps to auto publish blog posts from wordpress to facebook page.