Herman Cain leads Mitt Romney in the latest CBS News-New York Times poll, the latest of numerous surveys to show him on top of the Republican field -- but four out of five voters say their allegiance could still change.

Cain had 25 percent support among Republican primary voters and Romney had 21 percent, with a margin of error of plus or minus four percentage points. They have both gained support since the last CBS-NYT poll in early October, when they were tied at 17 percent, but Cain has managed to take the lead outright since then.

Newt Gingrich had a surprising third-place finish, but he remained far behind the two front-runners with 10 percent support. Ron Paul came in fourth with 8 percent, followed by Rick Perry with 6 percent, Michele Bachmann with 2 percent, and Rick Santorum and Jon Huntsman with 1 percent each.

The candidates' overall rankings tended to match their rankings among voters who identify themselves as Tea Party supporters, underscoring the clout the Tea Party continues to have, in spite of sharp decreases in the number of people who say they support it.

Cain had 32 percent support among Tea Party supporters, nearly double the 18 percent he registered just a few weeks ago and more than four times his result in mid-September. Romney had 18 percent support in the latest poll, up from 12 percent in September, and Perry has crashed from 30 percent support in September to 7 percent support now.

But there is plenty of time for the race to change, as about 80 percent of Republican primary voters surveyed said it was too early to say for sure which candidate they would support.

The dramatic changes in the poll results just in the past month underscore how volatile the race for the Republican nomination is.

Two months ago, in August, Bachmann was riding high on her victory in the Ames Straw Poll in Iowa, with support as high as 15 percent; now, she barely registers. A month and a half ago, Perry seemed unbeatable, with double-digit leads over Romney in some polls.

Through late September, hardly anyone had heard of Herman Cain, and very few people thought he had a chance of winning the nomination. Now, he is a front-runner. But will he stay there?