Sen. Lindsey Graham (R-S.C.) leads primary poll. (Chip Somodevilla - GETTY IMAGES)

Sen. Lindsey Graham holds a wide lead over a crowded field of challengers in South Carolina's June Republican primary, according to the first independent poll in the contest

A new Winthrop poll finds Graham garnering 45 percent support among likely voters in the open GOP primary, followed by Lee Bright at 9 percent, Nancy Mace and Bill Conner at about 4 percent and Richard Cash at 3 percent. Graham's sub-50 performance wouldn't be enough on Election Day to avoid a runoff with his top challenger, but he could easily clear that bar by garnering a fraction of the more than one in three voters who are currently undecided (35 percent).

Tea party supporters account for 57 percent of likely primary voters and are a weak spot for Graham, who wins only 34 percent of this group. Bright performs slightly better among tea party backers than voters overall (14 percent vs. 9 percent), but no candidate has galvanized the movement's support (moreso than Graham). 

One key strength for Graham is his general popularity with Republican likely voters. Asked their general feeling toward the senator, positive ratings of Graham outnumber negative ones by more than 2 to 1 (59 percent positive, 26 percent negative, the rest neutral or unsure). The poll did not include recent entrant Det Bowers, who joined  the race earlier this month. Winthrop said it did not ask about Bowers because he had not raised money by the time the questionnaire was prepared.

The Winthrop poll was conducted February 16-23 among 901 registered voters screened as likely to vote in the Republican primary. The sample contacted respondents using a combination of voter list-matched phone numbers and random digit dialing of cellular and landline phones. Full methodology is available here.

Peyton M. Craighill contributed to this report.