It seems that the Xbox Live service is not working at this point in time, and Microsoft did mention that they are well aware of the issues surrounding Xbox Live at this moment, where the service has not been working for some time already. According to the XBL status page, it mentioned that “users may experience difficulties signing into Xbox Live from an Xbox console”, and this applies to those who attempt to sign into Xbox Live from Xbox.com as well. Microsoft’s notice continued, “We are aware of the problem and are working to resolve the issue. We apologize for any inconvenience this may cause and thank you for your patience.”
To look at things on the bright side, at least this happened today instead of July 4th, where you most probably looked forward to that day in order to get as much gaming done as possible as there was no work for you to contend with. Hopefully Microsoft will be able to get things up and running as soon as possible.