A new poll from South Carolina shows a remarkable rise in support for John McCain, but with many Republicans still not having firmly decided how they will vote.

The latest Palmetto Poll, conducted by Clemson University between January 9 and 15, shows McCain in the lead with 29 percent – up from 11 percent in a Palmetto Poll last November. Mike Huckabee is in second place with 22 percent – up from 13 percent last November. Mitt Romney is in third, with 13 percent – down from 17 percent in November. And despite his recent efforts, Fred Thompson is in fourth, with 10 percent – also down from November, when he had 15 percent support. Rudy Giuliani is in disastrous shape, down to three percent from nine percent in November and 18 percent (a virtual tie for the lead) last August.

Seventeen percent of those surveyed said they were still undecided. But when the Palmetto pollsters asked those who did support a candidate whether they were sure of their support or whether they might change their mind before the primary, 46 percent said they might change their mind.