Xbox are hard at it trying to get this issue resolved ASAP, so sit tight, play some campaign and things will be back to normal soon.
“Hi Xbox members, we know some of you have been experiencing issues with your Friends list, unlocking achievements or sending/receiving messages or game invites. We want you to know we’re hard at work trying to get this resolved and we will update you as soon as we have more information. Thanks for all your patience while we get everything back to normal.”
You can check on the status of the service via the link below and get further details about the source of the problem once they resolve it.
Thanks for the update Xbox Live.