Did VP Biden exaggerate his role in 1983 Social Security reforms?

ABC News’ Jake Tapper reports:

Asked about Medicare reform, the vice president said, "Look, I was there when we did that with Social Security in 1983. I was one of eight people sitting in the room that included Tip O'Neill negotiating with President Reagan. We all got together and everybody said, as long as everybody's in the deal, everybody's in the deal, and everybody is making some sacrifice, we can find a way."

So did Biden exaggerate his role in the 1983 reforms? If you can’t already guess the answer to that question, read the full story to find out…