A Winthrop University poll released Wednesday shows Nikki Haley losing badly in South Carolina, her home state, with a little more than a week before the state’s Republican primary.

Nearly two-thirds of likely Republican primary voters, 65 percent, said they supported former President Donald J. Trump, and only 29 percent said they supported Ms. Haley. Those numbers are very close to the average results of recent polls of South Carolina.

After receiving 19 percent of the caucus vote in Iowa and 43 percent of the primary vote in New Hampshire, Ms. Haley has rested her argument for her campaign’s viability on the premise that she may not be beating Mr. Trump yet, but she is gaining ground. In an interview with NBC last month, she said of her performance in South Carolina, “I don’t think that necessarily has to be a win, but it certainly has to be better than what I did in New Hampshire, and it certainly has to be close.”

The poll’s fine print was also bad for Ms. Haley: Only 49 percent of registered voters, including Republicans and Democrats, said they had a favorable opinion of her, down from 59 percent in the last Winthrop poll in November. The drop was sharpest among Republicans, 56 percent of whom had a favorable opinion of her, down from 71 percent in November.