I'm not clear on what your problem is. OneCare performs a scheduled scan every day and a full scan as part of Tune-up. If OneCare is active and in green status, it is protecting the PC.
If it found threats and wants you to run a full scan, that isn't online, so I'm not sure what you are being prompted for. What is the exact message and when does it happen?
-steve
Microsoft MVP Windows Live / Windows Live OneCare & Live Mesh Forum Moderator