I've spent a lot of time to find the right solution for this.The best information I could find so far is from here: https://wordpress.stackexchange.com/questions/191258/return-scheduled-posts-with-wp-rest-api
I am using Jetpack for the REST API and this how it looks like for published posts:https://public-api.wordpress.com/rest/v1.1/sites/MYDOMAIN.com/posts/
Apparently you need to be logged in as a user that has the edit_posts capability. With that capability, you also get access to the private query vars, including post_status.
But the post doesn't explain how to include a logged in user in the REST API call so that I can get scheduled/future posts.
Thanks