Each of the candidates, with the exception of Ron Paul, planned to meet at a forum in Charleston on Saturday.
Meanwhile in Texas, more than 150 conservative Christian leaders voted to support Rick Santorum.
Many conservatives think Romney is too moderate. However the dynamics that lifted Romney to wins in Iowa and New Hampshire seem to be working for him in South Carolina, a state often described as too evangelical and culturally southern for his background.
But on the surface, at least, Romney is well-positioned with a week to go. If he wins South Carolina, only a seismic change in the campaign will keep him from becoming the nominee.
The next primary, on Jan. 31, is in Florida, a sprawling and expensive state where Romney's superior money and organization could essentially put the matter to rest, kicking off the general election against President Barack Obama.
The Associated Press contributed to this story.