Plugin to alert users about new postings

Hi,
I am looking for a plugin that akin to the way social media sites alert users that new postings have been listed. Rather than describing the posts, it simply says there is a new post and you have an option to log in to your account to view the updates. We have an auto-newsletter setup but it sends after each and every post as well as displays the content of the most recent post.

Is this possible with a wordpress plugin?
Thanks