I got this problem solved this moning because i also had it. Solution:
If you are having 'Two-Step Verification' enabled on your live account then turn it off and then try to login to xbox live though windows 8 or 8.1 apps & games e.g Pinball FX2 etc.
After logging in enjoy, if you want to then re-enable the 'Two-Step Verification' and the application will ask you to authorize, then what are you waiting for? Authorize via code or what method you use and u will be eligible to sign in to xbox live and problem shall resolve!