Mitt Romney and Herman Cain
Former Massachusetts Gov. Mitt Romney and businessman Herman Cain are in a statistical dead heat in the Iowa caucuses and in South Carolina's first-in-the-south primary. Reuters

Mitt Romney is leading in four early Republican primary states, but Herman Cain is close on his heels within the margin of error, making his position tenuous.

A CNN/Time poll released Wednesday shows Romney, a former Massachusetts governor, ahead in Florida, Iowa, South Carolina and New Hampshire.

Romney's biggest leads are in Florida and New Hampshire, in front of the pack with 30 percent and 40 percent of the vote, respectively. In Iowa and South Carolina, Romney has 24 and 25 percent of the vote, respectively.

For the Iowa caucus and South Carolina's first-in-the-south primary, businessman Herman Cain is within single digits of Romney and well within a five percentage-point margin of error with 21 and 23 percent of the vote.

The poll also highlights the fluid nature of the GOP primary.

Only about a third of all respondents in the surveys say their minds are made up, CNN Polling Director Keating Holland said.

More than 60 percent of Republican voters in Iowa said they might change their mind about their preferred candidate. In South Carolina, more than half said they might pick another candidate. In Florida, half of Republican voters surveyed said they may change their mind versus the 28 percent of voters sure of their 2012 pick.

Even in New Hampshire, where Romney is the favorite son, slightly under half of the registered Republicans surveyed were open to another candidate. Only 35 percent said they are definitely supporting their choice for the GOP presidential nod in 2012.

Beneath Romney and Cain in the four primary states are former House Speaker Newt Gingrich, Texas Gov. Rick Perry, Rep. Ron Paul of Texas and former Utah Gov. Jon Huntsman.

In Florida, Gingrich and Perry are tied with nine percent of the vote. For the Iowa caucuses, Paul takes 12 percent of the vote, with Ginrich and Perry tied for fourth with 10 percent of the vote.

In South Carolina, Paul edges Perry 12 percent to 11 percent. In New Hampshire, libertarian icon Paul has 12 percent of the vote, as Huntsman, a former U.S. ambassador to China in the Obama administration, takes six percent--his best showing in the early primary states.