WASHINGTON (Reuters) - Former pizza executive Herman Cain is now tied with Mitt Romney for the lead in the race for the 2012 Republican presidential nomination, while former front-runner Rick Perry has taken a steep fall, according to a CBS News poll released on Tuesday.

Cain had 17 percent support among Republican primary voters, up from just 5 percent two weeks ago, the poll found.

That tied him with Romney, the former Massachusetts governor, whose support essentially held steady.

Cain, the lone African-American in the Republican field, upset Perry in the Florida straw poll last month, dealing a disappointing loss to the Texas governor two days after Perry's shaky debate performance.

Perry's support has fallen 11 percentage points to 12 percent -- down from 23 percent two weeks ago, according to the CBS News poll.

Eighty percent of Republican primary voters said the candidates' debate performances were important to them and 58 percent said they had watched the debates.

Farther back in the poll, Newt Gingrich had 8 percent support, Ron Paul 7 percent, Michele Bachmann 4 percent, Rick Santorum 3 percent and Jon Huntsman 2 percent. Eighteen percent said they were undecided or unsure.

Among other findings, 32 percent of Republicans polled said Romney had the best odds of defeating President Barack Obama, a Democrat, in the 2012 presidential race. Twenty-one percent said Perry had the best chance of winning the White House and 8 percent said Cain.

The telephone poll of 1,012 adults was conducted from Wednesday to Sunday and had a margin of error of plus or minus 3 percentage points.

A Washington Post-ABC News poll released earlier on Tuesday had Romney in the lead with 25 percent support, unchanged from a month ago. Perry and Cain were tied for second with 16 percent -- a 13-point drop for Perry and 12-point rise for Cain since early September.

(Reporting by JoAnne Allen; Editing by Peter Cooney)