According to the internal poll, Colbert Busch's approval rating is at 48 percent in the district. Twenty-four percent of voters disapprove.
The poll's sample gave Republicans a 14-point edge over Democrats in the electorate, roughly their edge in the average election in the district.
"It is clear the 1st district is hungry for the real world leadership and business experience that Elizabeth would bring to Washington and her focus on common-sense solutions, fiscal responsibility and creating new jobs clearly resonate with voters," Colbert Busch spokesman James Smith said.
Sanford is the favorite to win Tuesday's primary runoff against attorney Curtis Bostic (R), who Colbert Busch led by a wider margin in the poll.
The poll of 400 likely special election voters was conducted by Lake Research Partners from March 25-27 and had a margin of error of plus or minus 4.4 percentage points.