Microsoft has confirmed that people who have downloaded the free preview version of Office 2013 and who might be seeing some early expiration dates can ignore them From Neowin:

For the past few days, we have heard that some people who have downloaded and used the free Office 2013 preview version via Office 365 have been seeing that their trial would be expiring very soon. Some reports, such as the one we spotted at McAkins Online, said that the preview build would be expiring today, January 16th. Our own preview version of Office 2013 shows a expiration date of January 20th when we checked out Microsoft Account info.

Well, we checked in with Microsoft and and finally received a response today. The short answer is that Office 2013 preview users don't have anything to worry about.

 Microsoft to Office 2013 preview users: ignore those expiration dates