DeMint, who has been strongly identified with the Tea Party, is stepping down to head the conservative Heritage Foundation think tank in Washington.
The Public Policy Polling survey said 20 percent of those surveyed wanted the Comedy Central star to fill the outgoing Republican's shoes, with his closet rival, U.S. Rep. Tim Scott, D-S.C., at 15 percent.
The poll said Republican Nikki Haley is one of the most unpopular governors in the nation, with only 42 percent approving of her job performance compared with 49 percent who disapprove. That makes her 35th in popularity of the 43 sitting governors PPP has asked about in polls.
She had trouble with Democrats and independents. Among Republicans, 70 percent approved of her and 22 percent disapproved.
Among Democrats, 32 percent say they'd like Colbert to be picked to fill DeMint's seat, 19 percent picked Republican former state first lady Jenny Sanford, and no one else was in double digits.
Among state independents, Colbert has a 15 point lead for the appointment, getting 28 percent to 13 percent for Scott, and 12 percent for Sanford. A PPP release on the poll did not give GOP preferences.
PPP surveyed 520 South Carolina voters Dec. 7-9. The margin of error is 4.3 percentage points. PPP said the poll was not paid for or authorized by any campaign or political organization.