Perhaps I just didn't notice during setup, but Sharepress charges money to post anywhere but on a default Facebook page of it's choosing.
Also, numerous instructions regarding generating an API and API Secret code thing from Facebook were very complex, or simply wrong because the options described do not appear where the instruction say they will be. Perhaps this is due to individual settings (as in a new account), or with the new timeline interface at Facebook, or just plain wrongness.
After spending hours and hours and hours trying to get everything set up just so... the Sharepress plugin wouldn't work as I needed it to without me paying for an upgrade. Respect to the developer, but it was...
After many more hours I figured out this much, much easier solution:
1. Install the "Twitter Publisher" plugin so all of your wordpress posts are sent to your Twitter account. See the plugin instructions to easily have your post titles (with a link) automatically cross-posted to Twitter. There are other Twitter plugins that work, I just think Twitter Publisher is the easiest to setup for this single purpose, and is reliable.
2. Login to your Twitter account, if you are not already.
3. Find the Settings link at top right of Twitter. (As of this writing, you have to click on an icon with a reverse silhouette of a person's head, to open a small pull-down menu with "Settings" as a choice.)
4. Now, from your Twitter settings page, choose from the column (currently) at left, which reads, "Profile."
5. Scroll down a bit, and on the right, you'll see a button that reads "Facebook: Post your tweets to Facebook". Click the button.
6. If you aren't already logged into Facebook, a popup window will allow you to login to Facebook. Once logged in, approve the settings offered to you.
7. Twitter will then ask you which page you want your linked tweets to appear on (which is a feature that Sharepress wants you to pay to upgrade for). Choose where you want your tweets to appear on Facebook via the little pull-down menu.
8. Save settings.
"It works! 88 miles per hour!" - Doc Emmett Brown