The post draft to be saved.
Receive notice: "Saving of draft failed".
Unable to save draft.
Upon publishing post, receive notice: "Post scheduled for Invalid date!" and post is scheduled for date originally scheduled.
Tested and confirmed that after canceling scheduling for a draft post I see a "Saving of draft failed" notice at top right, no errors in the console, and this API call and response:
12125?http_envelope=1&context=edit
public-api.wordpress.com/rest/v1.2/sites/5276229/posts
{"code":400,"headers":[{"name":"Content-Type","value":"application\/json"}],"body":{"error":"invalid_input","message":"Invalid request input"}}

Seen at https://wordpress.com/post/design5279.wordpress.com/12125 (WP.com Simple / Business Plan) using Chrome 66.0.3359.139 on macOS 10.13.4.
@Automattic/tanooki will look into this
@jsnajdr You might be interested in looking into this issue while in the neighborhood. Here's some notes that @Automattic/tanooki had from our recent team call where we discussed this issue a bit...
Request gets sent with:
{
date: null
}
and response:
{
"code":400,
"headers": [
{
"name": "Content-Type",
"value": "application\/json"
}
],
"body": {
"error": "invalid_input",
"message": "Invalid request input"
}
}
This is because the date: null results in an empty input array that is rejected by the API endpoint.
One potential solution is to modify the endpoint to accept either a value or null for date:
'date' => '(ISO 8601 datetime|null) The post's creation time.',
That would probably allow the null to be passed through so that the endpoint could handle it.
The WP.com endpoint (wpcom-json-api-update-post-v1-2-endpoint) does some magic with dates, e.g., resetting it to "now" when transitioning from "draft" to "publish" or from "scheduled from future" to "publish now".
Also, the core wp_update_post function can clear the date in some circumstances: look for the edit_date param and the $clear_date variable.
However, I don't see the capability to reset the date of a post that already has an explicit date set in the code. The wp-admin editor UI also doesn't have the "Publish Immediately" option.