In ruby, at least, there are some good tools to automate this for you. Using, say, vcr, you can automatically "record" your API calls (into "cassettes") as your tests run; these data are then used when you run your unit tests subsequently. When you plan to integrate/push, simply delete the "cassettes" and run your tests again. That way, any API changes are picked up prior to integration.

I have a suite here that takes about 3 minutes to run from scratch, but just over 1 second as unit tests.