Google sues the US government over Microsoft favoritism
From that information, it sounds like Google has a pretty good case that the government illegally restricted competition. Google met with the DOI to discuss why the project was limited to Microsoft solutions, and they were told that Microsoft was the only company that provided "unified/consolidated email" and "enhanced security." In its filing, Google argues that this is completely false, and that competing products (like Google's own) meet the DOI's needs.
Here's the catch, though: the case might not have any legs, because Google doesn't even have the proper contracts to do business with the government, so it may never have been in the running to begin with. Expect the government to bring up the issue of Google's standing to sue (or lack there of) in its response.