I have my blog posts set to go live at specific dates/times. I'd like to have these posts auto-post to Facebook when they go live.
Is there a method to do this or an application or plugin that supports this?
By providing the RSS feed of your blog to Ifttt.com you can have it post to Facebook & other popular social media sites
You can also use the sharing settings in your WP theme to automatically post to FB, Twitter, RSS, LinkedIn, Google+, Tumblr... In your dashboard go to Settings, one of the options should be Sharing. Once there you can enter the login credentials and any pages you own will be listed with your personal page -- allowing you to choose where you want WP to post.
The majority of WordPress themes, free or paid, have sharing included today. If you have an older theme, you may need to update to the latest version.