DeMint, speaking on "Fox News Sunday," said the Tea Party movement represents "just the tip of the iceberg of an American awakening" that will show itself come November.
"Lindsey's a great friend, but he's wrong on this," DeMint said. "It's really a matter about success or failure as a country and I think Americans are going to show in November that this isn't going away."
DeMint was responding to comments Graham made in The New York Times Magazine. In the article, Graham suggested Tea Party activists don't know what they want, describing as "very, very contentious" the meetings he's held with them.
"The problem with the Tea Party, I think it's just unsustainable because they can never come up with a coherent vision for governing the country. It will die out," he was quoted as saying, adding that Ronald Reagan would have had a hard time "getting elected as a Republican today."