Republican pollster Bill McInturff, who conducted the poll with Democrat Peter D. Hart, said Perry's fall and Cain's jump ahead -- from 5 percent in the previous poll in August to 27 percent in the new one -- is probably not the last dramatic shift in the race. Businessman Donald Trump, U.S. Rep. Michele Bachmann, R-Minn., and others have briefly seized the hearts of Republican voters before slipping.
"There is still a long, long, long time to go," McInturff said.
Romney polled 23 percent in both October and August, while Perry dropped to 16 percent from 38 percent. Libertarian Rep. Ron Paul, R-Texas, was the only other candidate in double digits with 11 percent.
Cain is popular with two important groups in the Republican base. Among Tea Party supporters, 69 percent view him favorably and 5 percent unfavorably while his score is even higher -- 72 to 2 -- among those who say they are "very conservative."
Hart described Romney as "acceptable" to Republicans. His favorability rating is 55 percent to 20 percent among Tea Party supporters, and 60 to 19 among the "very conservative."
Democratic President Barack Obama led in theoretical match-ups with Romney, Perry, Cain and a generic Republican. His advantage against Romney or a generic Republican was only 2 percentage points, but it grows to 11 points against Cain and 12 against Perry.