How about using scheduled publishing option in WP posts?
https://en.support.wordpress.com/posts/schedule-a-post/
Possible scenario should be something like this:
1. Make multiple posts (eg. Monday, Tuesday … Sunday) all placed into one category (eg. Week). Every single post will be scheduled to automatic publishing at 00:01 at corresponding date.
2. Place the widget into desired sidebar and call
category=Week
post_per_page=1
post_status=published, scheduled (press and hold CTRL for multi select)
post_type=post
entry_container=div (probably, it’s up to You)
3. click Save and check front page
Please note that scheduled time is formatted as 00:00-23:59, so never use am/pm formatting. You should also check Your WP time settings if it is correct.
Also note that if Your post content is intended to be seen on different time zone areas, this will be very bad approach.
Hope this will be helpful.
