Here's a guide on removing the plug from the jack on a Macbook, shouldn't be much different on your iPhone.
The page is in Spanish, but there's pictures and if you run it through a translator you should be good to go.
Thank you so much! I translated the Spanish into English. The concept is what helped me. What broke off in my iPhone was the inside of the connection at the tip of the audio cable. Just a pencil thin piece of metal was sticking up inside the port. I tried using the tubing and a thin piece of metal but there wasn't enough surface on either end to grab and pull out the end of the connector. What I ended up doing was putting Krazy Glue inside the end of the cable and putting that back into the port. I waited about 15 minutes and pulled it straight out and it worked!! The key is not to twist at all, just pull straight out.
I am so glad you gave me the suggestion!!