I see two solutions of doing it:
1) Use Asterisk with the auto-dial and swift features:
2) Use a service provider such as Telemessage: http://www.telemessage.com/landLineSms.html
If you're going to spend money then you might look at CA's product called Automation Point. We've used it for years now. It is solid as a rock.
The server uses this card http://www.dialogic.com/products/tdm_boards/media_processing/D4PCI_Boards.htm
The software dials any number and speaks the message. It can be set up to try an Office Phone (no answer) try Cell Phone (no answer) try Home Phone (answer) and interact with the person from the phone pad. It's really cool stuff. And includes a way to escalate if no contact has been made.
But this is pretty much an enterprise solution and has enterprise pricing to boot.
lchance, have you actully used it to call you with Solarwinds Alerts? This looks like a Server/mainframe monitoring application, but has the call feature that I am looking for.