Hi Douglas,
If you import the RestServices Module and the Community Commons module into your project, you can exactly do this using the 'get' function. It will also parse the json for you if you setup your domain model correctly. See
Perform a get request: https://github.com/mendix/RestServices#get
Deserialize the json: https://github.com/mendix/RestServices#json-deserialization
Send the authentication data: https://github.com/mendix/RestServices#authentication
Edit: example of consuming a REST service can be found in this blog post