WASHINGTON — President Trump and Senator Lindsey Graham have established clear but not overwhelming advantages in South Carolina, a heavily Republican state that is showing signs of competitiveness this year, according to a new New York Times/Siena College poll.
Mr. Trump leads Joseph R. Biden Jr., 49 percentage points to 41, while Mr. Graham, who is facing the most serious challenge of his career, is winning 46 percent of the vote compared with 40 percent for his Democratic rival, Jaime Harrison.
The Senate race, though, may be even more competitive because the survey finds that 12 percent of Black voters are undecided, a vote share that is likely to favor Mr. Harrison, who is African-American. The poll has a margin of error of 4.5 percentage points.
No Democratic presidential candidate has carried South Carolina since Jimmy Carter in 1976, a streak that appears unlikely to be broken this year. But the combination of Black voters and white transplants there is poised to make the state more of a battleground than an afterthought going forward.
It’s this coalition of voters that’s pushing Mr. Trump’s advantage into single-digits, four years after he carried South Carolina by 14 points, and that has made the race between Mr. Graham and Mr. Harrison perhaps the most surprisingly close Senate matchup of 2020.
Still, South Carolina remains more conservative than its fast-changing neighbors, Georgia and North Carolina, and quite forbidding for Democrats. The state hasn’t elected a Democratic governor or senator since 1998.
While college-educated white voters in other Sun Belt states favor Mr. Biden or break even between the two presidential contenders, they favor Mr. Trump 50 percent to 38 percent in South Carolina. Even more stark, and for Democrats downright daunting, is the gap between white voters without a college degree: 77 percent favor Mr. Trump while just 18 percent support Mr. Biden.
There is far more uncertainty in the Senate race. After being one of Mr. Trump’s fiercest critics in the 2016 campaign, Mr. Graham has become one of his most loyal lieutenants.
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This shift, along with the skepticism Mr. Graham has faced from far-right Republicans because of his penchant for deal-making, has made him vulnerable to a challenge.
And Mr. Harrison, a former lobbyist who served as the South Carolina Democratic Party chairman, has emerged as a fund-raising dynamo: He just shattered the record for Senate fund-raising in a quarter, netting $57 million in the three months from July through September.
Jason Strickland, a 44-year-old Republican from Summerville, S.C., lamented Mr. Graham’s willingness to compromise, citing immigration as an example. Mr. Strickland criticized what he called Mr. Graham’s push for “amnesty,” a reference to the senator’s yearslong effort to broker a bipartisan immigration overhaul that would include a pathway to citizenship for millions of immigrants who are in the country illegally.
Mr. Strickland said he would unenthusiastically cast his ballot for Mr. Graham because the “biggest” factor in his thinking is his dislike for Mr. Harrison.
“I have a huge issue with the whole Black Lives Matter” movement, he said.
Adding another wrinkle to the Senate race is the presence of a Constitution Party candidate, Bill Bledsoe. While Mr. Bledsoe has withdrawn from the race and endorsed Mr. Graham, his name is still on the ballot. And Mr. Harrison’s campaign is spending money on advertising to trumpet Mr. Bledsoe’s conservative credentials and siphon off votes from Mr. Graham.
Mr. Bledose is garnering 4 percent in the survey while 8 percent of voters over all say they are undecided in the Senate race. Notably, 6 percent of South Carolina Republicans said they were undecided in the Senate contest while only 2 percent of them said the same about the presidential race.
Mr. Graham, seeking a fourth term, is capturing 89 percent of Republicans, a number he will need to increase to stave off Mr. Harrison’s challenge, given the likelihood of Black voters moving to the Democrat.
The good news for Mr. Graham as it relates to his own base is that he’s now on center stage in Congress, wielding the gavel at the Senate Judiciary Committee each day this week during Judge Amy Coney Barrett’s televised confirmation hearings.
Fifty-two percent of South Carolinians said they backed Ms. Coney Barrett’s confirmation while only 30 percent said they opposed it. The support for her was even higher among college-educated white voters, with 59 percent of them backing her appointment.
Notably, Mr. Graham fared better in the survey in the final two nights of polling calls to voters, after the Supreme Court hearings had begun. In the initial calls, starting last week, the Senate race appeared closely divided. But this week, Mr. Graham actually fared better among respondents than Mr. Trump.
Mr. Harrison’s fund-raising has also spurred more Republican donors to give to Mr. Graham, who raised $28 million over the past three months.
Still, Mr. Graham, who has scarcely faced a competitive race since he was first elected to the House in 1994, is in the fight of his political life.
Many South Carolina voters have soured on him. Forty-nine percent of voters said they do not think Mr. Graham is honest and trustworthy while 41 percent said they thought he was, according to the survey.
And while 40 percent of South Carolinians said they had a very favorable view of Mr. Trump, there was less enthusiasm for Mr. Graham. Only 26 percent of voters said they viewed him very favorably.
Among Republicans, the divide was even more pronounced: 79 percent of G.O.P. voters said they viewed Mr. Trump very favorably while only 54 percent of the state’s Republicans said the same about Mr. Graham.
The senator’s bet, however, is that serving as one of Ms. Coney Barrett’s most visible advocates and linking himself to Mr. Trump will be enough to survive the threat posed by Mr. Harrison.
Asked if they might change their minds about their presidential vote, 98 percent of South Carolina Republicans said they were definitely voting for their preferred candidate.
The race may hinge on the scale of the Black turnout and, in particular, whether it reflects the enthusiasm there was for former President Barack Obama or more closely resembles the 2016 race. In 2008, Black voters made up 25 percent of the South Carolina electorate. Four years ago, it was only 19 percent.
This poll is based on African-American voters making up 23 percent of South Carolina’s electorate.