In an appearance on "Fox News Sunday," Graham said the Illinois senator and likely Democratic presidential nominee made race an issue last week when he claimed the campaign of Republican presidential candidate John McCain would try to "scare" American voters because he has "a funny name" and "doesn't look like all those other presidents on those dollar bills."
McCain, Graham said, "doesn't have a racist bone in his body."
"And there's no doubt in my mind that what Sen. Obama is trying to suggest -- that he's a victim of something," Graham said.
Daschle, a South Dakota Democrat and an Obama backer, denied that Obama tossed race into the political debate.
"What he is saying is that he is a different kind of candidate, a different kind of leader, a person who has come to Washington with a different agenda, of someone who really does want to be a vehicle for change," Daschle said. "This is change vs. the status quo."