The change has almost entirely come among more conservative voters. Among those Republicans who identify as members of the Tea Party, Cain leads Romney, 24 percent to 17 percent, with Perry back in fourth place at 12 percent. Two weeks ago, Perry had nearly a third of the Tea Party vote, but recent criticism of his record and poor debate performances have damaged Perry's candidacy.
Cain, meanwhile, was a non-factor among Tea Party supporters two weeks ago, with only seven percent of the vote among those voters. Over the past two weeks, as Perry's support has dwindled, Cain's outsider profile -- he is the former CEO of the Godfather's Pizza chain -- appears to have resonated among Tea Party voters.
Despite Cain's rise, Republican primary voters are not yet quite convinced he is ready for prime-time. Asked which candidate has the best chance to defeat President Obama
in the general election, 32 percent choose Romney, and 21 percent say Perry. Just eight percent of Republican primary voters think Cain has the best chance to beat Obama.
Polls released early Tuesday from ABC News/Washington Post
and Quinnipiac University
also showed significant increases in Cain's support, while also showing a decrease in support for Perry.
The CBS News poll was conducted Sept. 28-Oct. 2, surveying 324 voters who say they plan to vote in the Republican presidential primary. The margin of error is +/- 5.4 percent.