The CBS poll, conducted Nov. 6-10, shows support for Cain has dropped since late October, when allegations of sexual harassment surfaced. Although 61 percent of Republican primary voters say the accusations against Cain won't make any difference in their vote, 31 percent say the allegations make them less likely to back him. Cain's support among women has dropped from 28 percent to 15 percent since October.
The CBS poll of 1,182 adults has a margin of error of plus or minus 3 percentage points.
A Marist poll puts Romney at the lead of the pack with 23 percent followed by Gingrich as 19 percent and Cain with 17 percent.
"The race for the GOP nomination has taken yet another dramatic turn," says Lee M. Miringoff, director of the Marist College Institute for Public Opinion. "Now, the top tier is crowded as Newt Gingrich has taken his place alongside Mitt Romney and Herman Cain. Could anyone imagine a more unsettled contest?"
Of the 1,026 adults questioned in the Marist poll, 17 percent said it was too early to tell who they will vote for, while 31 percent said they may change their minds.
The Marist poll, conducted Nov. 8-10, has a margin of error of plus or minus 3 percentage points.