The Harris Poll said among 355 adults who expect to vote in a Republican primary or caucus, 25 percent said they would vote for Giuliani, down from 34 percent in November.
About 21 percent of online respondents said they would vote for former Arkansas Gov. Mike Huckabee, who just last month had 9 percent support.
Still in third is former Massachusetts Gov. Mitt Romney with 18 percent, up 2 points over last month, and dropping from second place to fourth place is former Tennessee Sen. Fred Thompson with 16 percent.
Among 552 likely Democratic voters, 48 of respondents surveyed Dec. 7 and Dec. 17 said they would vote for Clinton while 30 percent said they would vote for Sen. Barack Obama of Illinois.
Former North Carolina Sen. John Edwards was still in third place, with 13 percent. The remaining Democratic contenders polled with 5 percent or less.
Notable deaths of 2014 [PHOTOS]