In the services section of the Google API console there are two services relating to drive development, SDK and API. When you create a new Drive SDK entry, Drive API service is not automatically enabled (which doesn’t make sense, I don’t see when you’d create a drive enabled application without using the drive API). Switch the Drive API service on for the project and try again.
@lurking_googlers I think a lot of people will fall for this, doesn’t it make sense to enable the API when the SDK is enabled?