Unfortunately yes, over-communicating can become an issue. I have found this area very difficult to measure, and therefore resolve, since what it may be interesting for some people may be an area of concern and conflict to others.
Personally, I have come across several issues when communicating potential changes to the project's allocation of resources. I have always thought that a transparency is the key for building the confidence of a team and awareness of what's going on in the project at different levels. However, there is the risk that team members perceive certain information as a threat to their jobs or misunderstand the purpose of senior management's decisions.
From my point of view I would keep communicating anything related to working packages, open issues, and current status of assigned tasks but I would discuss with my line management to set up a communications plan, delivered by a Communications Specialist (independent role that reports to a different level of management), for information like resource re-allocation (outsourcing plans specially), budget constrains, and any other sensitive topic.
In my current job we have a person in charge of releasing communications in reference to the overall status of the project via email and posts to our SharePoint site. Should there be any questions within my team we openly discuss them in our reviews and I address their concerns to my line management for further support. This helps me to reduce my level of involvement on any matters aside my duties.
Also see: http://www.scottberkun.com/blog/2010/how-to-stop-overcommunication/
