ROCK HILL, S.C. - Mitt Romney continued his criticism of former Speaker Newt Gingrich during an afternoon rally, accusing his GOP rival of jumping on the "bandwagon" of attacks started by President Obama.

"I think the president's attack on free enterprise and capitalism and success is beneath him," said Romney, speaking at a rally at Winthrop University. "By the way, I have been disappointed that even in our race that some Republicans have jumped on that bandwagon. Recognize it's not the way to build a strong economy to tear down fellow Americans or to attack capitalism."

"My goodness, I listen to Speaker Gingrich the other night talking about the enterprises I've been associated with," said Romney, mentioning Gingrich by name for a second time today. "I am proud of the fact that I've worked in the private sector, that I have achieved success, that we were able to build jobs in America, and I am going to keep using that experience to make sure that we build jobs for the entire country."

Romney's remarks came just as a new CNN/Time Magazine/ORC poll shows him in place to win the support of 33 percent of likely South Carolina GOP voters, while Gingrich gets 23 percent, Rick Santorum 16 percent, Ron Paul 16 percent and Rick Perry 6 percent.

But earlier this month, Romney was leading Gingrich by nearly 20 percentage points in South Carolina, a gap that has shrunk in just two weeks and has been noted by the Romney campaign.

Romney also hinted during the rally at what kind of ads his campaign might run against President Obama, should he become the Republican nominee.

"After he was inaugurated, we're going to play this on TV time and time again in our ads, he said if he couldn't get this economy turned around in three years, he'd be looking at a one-term proposition," said Romney, referring to an interview Obama did on the Today Show, an appearance Romney uses frequently on the trail.

"Well, we're here to collect," said Romney.