So I started up the demo and it's asking me whether I'm a Spacer, Colonist, or Earthborn and whether I'm Ruthless, a War Hero, or a Sole Survivor. Based on this forum thread it appears these choices didn't matter in ME1, it was barely mentioned, which seems strange given everything I've heard about your choices impacting the game. Does it matter more in ME3? Does it limit what you can do or significantly impact any character's dialog or attitude towards you?
I played a Spacer War Hero in my Mass Effect 3 playthough, so while I can't speak for the other origins, the Spacer Pre-Service History (mentioning Shep's mother, who's captain of another ship in the Alliance Navy) came up a lot less than the Background (Hero of Elysium against the Skyllian Blitz) did.
For the demo in particular, it's practically irrelevant; the only reason it's in there at all is because the demo features the tutorial level, and it was probably more trouble than it was worth to remove it.
Neither has a huge change on the story - in many ways, it had the most effect(ha!) in Mass Effect 1, simply because each Pre-Service History had an associated assignment, while later games did not.