A News post must be "Published" in order to send an SMS message at a scheduled time.
It is possible to set a scheduled time for a News Post to go live, but then save it without publishing. As with pages in Page Manager, publishing is a required step in order for content to be made visible to site users; even if a post date is set, if a post is unscheduled it will not go live. Since SMS messages are sent when a post goes live, they are never triggered by Unpublished posts.
Double check the settings for the post - if it appears in the "Recent Drafts" section of the News Manager dashboard rather than the "Upcoming Posts" section, go back in and make sure that it's published.