Backing for Romney jumped to 37 percent, a 17 percent increase since early December, according to a Time/CNN/ORC poll of likely South Carolina primary voters conducted on Wednesday and Thursday.
If Romney follows his slim victory in Iowa's caucuses with a win in next week's primary in New Hampshire, where he has a solid lead, a triumph in South Carolina on January 21 could give him a nearly insurmountable edge as he vies for the nomination to oppose President Barack Obama in November's election.
The South Carolina poll showed support for Romney from a range of Republican voters, with backing from 35 percent of born-again Christians, 32 percent of Tea Party movement backers and 37 percent of self-described conservatives, Time said.
However, 49 percent of likely voters said they were still open to changing their minds, and Romney is expected to face a fierce fight for the southern state's votes from rivals portraying him as northeasterner who is too moderate.
Support for Rick Santorum, a socially conservative former senator from Pennsylvania, leaped to 19 percent from 4 percent in the South Carolina poll, conducted after Iowa's caucuses on Tuesday, where he came a surprising close second to Romney.
Santorum's gain in South Carolina came partly at the expense of Newt Gingrich, a former speaker of the U.S. House of Representatives who was a close third at 18 percent, but who plunged from 43 percent support last month.
Texas Congressman Ron Paul also gained in the southern state, the poll said, as his share doubled to 12 percent. Texas Governor Rick Perry had 5 percent.
Ahead of Tuesday's primary in New Hampshire, a 7 News/Suffolk University tracking poll of likely primary voters showed Romney, a former governor of neighboring Massachusetts, with a strong lead of 40 percent.
Paul was in second in New Hampshire at 17 percent, according to the poll conducted on Wednesday and Thursday. Santorum's backing rose to 11 percent, up from 8 percent at the beginning of the week, it said.
Since finishing narrowly behind Romney in Iowa, Santorum has also moved ahead of Gingrich and former Utah Governor Jon Huntsman in the New Hampshire survey. Gingrich was at 9 percent in the Suffolk poll, and Huntsman, who was endorsed over Romney by the Boston Globe newspaper on Thursday, had 8 percent backing.
One percent of the New Hampshire voters surveyed backed Perry, and 15 percent were undecided.
The New Hampshire poll was based on telephone interviews of 500 likely voters in the Republican primary and has a margin of error of 4.4 percentage points.
The South Carolina poll surveyed 1,519 adults, including 485 likely voters, by telephone on January 4-5. It carries an error margin of 4.5 points.
Another New Hampshire opinion survey, conducted on Wednesday, showed a Santorum bounce and a tighter race overall in New Hampshire.
The Washington Times/JZ Analytics Poll of almost 500 voters put Romney ahead with 38 percent, followed by Paul at 24 percent and Santorum at 11 percent. Ten percent of voters were undecided.