When new people sign up or sign a petition, how can we tell where that individual came from. Analytics gives you a general idea, but if two people sing up during the same part of the day, one following a link from Facebook and one from Twitter, how can we know which is which?
While you can't see this information directly in NationBuilder (it's actually quite a challenge as Facebook deliberately blocks referral info for privacy reasons, and most people use Twitter through a mobile or other app the doesn't include referral info), there is a little known feature in NationBuilder that will let you use the Google Analytics tracking codes you refer to to map them back to any action people take on your site.
Any time someone signs a petition, donates, or does anything that involves submitting a form, a "/goal/[page_slug]" gets sent to Google Analytics. You can set that up as a goal in GA and then use all the standard GA features to do analysis. So if your donation page is at /donate, then /goal/donate would be the goal.
There is a screencast on this here: http://nationbuilder.com/how_to_setup_google_analytics