Reince Priebus said Cain was having trouble raising cash and his numbers had stalled despite the popularity of his 9-9-9 message.
"Certainly his numbers were falling over the last few weeks and he was having trouble raising money, and I think it's only natural, if you're numbers are falling, you can't raise the money to stay in the race that you'd get out of the race," he said.
Cain was battling allegations of sexual harassment and a claim that he had a 13-year extramarital affair. The Georgia businessman has denied the accusations, and said he had provided financial help to the woman claiming the relationship as well as a male friend.
On Saturday, Cain dropped out of the race, saying that while he was innocent of the charges, he didn't want to expose his family to any more emotional hardship. He said he is going to stay involved to force change in Washington.
Rep. Michele Bachmann, who appeared on "Fox News Sunday," said Cain brought "much energy and goodwill to this race" and was an intriguing candidate.
"The race was better for having Herman Cain in the race. I really enjoyed talking to him all throughout the race," she said.
Priebus said Cain might have a big role to play. But Priebus told NBC's "Meet the Press" that depends on a politician having money and being to get out into the public.