I was having this very same issue and it turned out it was the IP address. I had to find my Arduino's IP by following these instructions: http://www.instructables.com/id/Arduino-Ethernet-Shield-Tutorial/step3/Get-started/
To figure out what IP address has been assigned to your board, open the DhcpAddressPrinter sketch. This can be found at:
File --> Examples --> Ethernet --> DhcpAddressPrinter
Once I ran the above example and added that IP to my Simple Post it went right on through to Twitter.
The website that is running the app and where you get your Oauth token takes care of that SSL issue.