Sen. Lindsey Graham’s emergence as President Trump’s horse whisperer has likely helped cement his position among South Carolina Republicans — but Democrats say it’s created an opening for them to take his seat in 2020.

It would be a stunning upset in a solidly red state, where Mr. Graham won last time with 55 percent of the vote.

But Democrats say the senator appears to be grasping at Mr. Trump’s coattails in a bid for attention that has undercut his reputation as a maverick and could potentially cost him the support of crossover Democrats and middle-of-the-road independents.

“To me, it just comes across that [what’s] most important for Lindsey is not his role as senator,” said Jaime Harrison, former chairman of the state Democratic Party and a likely Graham challenger. “It is whether he is in the mix, whether there is a microphone or TV camera there. For Lindsey, that is what it means to be relevant.”

Others see Mr. Graham’s bond with the president in more nuanced light, saying he’s been an equal-opportunity enrager over his career.

“There is an almost schizophrenic way that Lindsey Graham has handled his politics in recent years,” said Charlie Cook, of the Cook Political Report. “Watching Graham is like watching a sailboat tacking first to port, then to starboard, then to port then back to starboard, repeating again and again.”

Those tacks include having been an impeachment manager in the case against President Bill Clinton, then siding with the ultimate maverick Sen. John McCain, earning the nickname “Lindsey Grahamnesty” for his work on immigration, yet delivering the most forceful defenses of Mr. Trump’s judicial nominees, his emergency wall building declaration and his foreign policy.

The support has overshadowed his critique of Mr. Trump’s decision to disengage in Syria and his response to the violent white nationalists rally in Charlottesville in 2017.

“When I don’t agree with the president, I will tell him,” Mr. Graham told The Washington Times. “But I unashamedly want him to be successful and got a good working relationship with him, and I think that is overall a benefit.”

It’s likely a smart place to be in a state that hasn’t voted Democratic in a presidential election since Jimmy Carter carried it in 1976, and where his bigger electoral challenges have come in the primary.

Chip Felkel, a South Carolina-based GOP strategist, said Mr. Graham is a political pragmatist who recognizes that he won’t lose as much as support as he gains from the relationship.

“The challenge for Graham was always expected to be the right in a primary,” Mr. Felkel said. “He has shored that up.”

The friendship between the veteran senator and the political outsider seemed unlikely during the 2016 presidential campaign — particularly after Mr. Trump mocked the idea that Mr. McCain, Mr. Graham’s best friend on Capitol Hill, was a hero for getting captured during the Vietnam War.

By the time the dust settled, Mr. Graham had called Mr. Trump a “race-baiting xenophobic bigot,” and Mr. Trump had shared Mr. Graham’s cellphone number at a campaign rally — forcing him to get new digits.

“President Trump and I did not start off well,” Mr. Graham said with a chuckle this month at the Conservative Political Action Conference. “I remember meeting him after he got elected and saying, ‘Hey, Lindsey, I don’t have your phone number’ and I said, ‘There is a reason for that.’

“So I have given him my phone number and trust me he uses it, and I couldn’t be more proud of the fact that he talks to me and he asks my opinion, and we have a lot in common now. I like him and he likes him,” Mr. Graham said.

Mr. Harrison, who has been encouraged to run by Senate Minority Leader Charles E. Schumer, said the key to defeating Mr. Graham is to win over the independents, conservative Democrats and moderate Republicans who held their noses while voting for Mr. Trump.

“Those people are not the biggest fans of Donald Trump and the rhetoric of Donald Trump and those people are asking what has happened to Lindsey Graham,” Mr. Harrison said. “As long as he wants to tie himself to Donald Trump that is great, but you take the good with the bad and there is a lot of bad.”

Mr. Graham welcomes the possible fight with Mr. Harrison, saying that matchup would offer voters a choice of candidates with clear differences on issues like the confirmation of Supreme Court Justice Brett M. Kavanaugh.

“Here’s the deal,” Mr. Graham told The Times. “He thinks that what I did in Kavanaugh was bad, I think it was good.

“I voted for Democratic nominees, and I never thought of doing to them what they did to Kavanaugh, and I think most South Carolinians are going to see it the way I do, and we should all want our president to be successful,” the GOP senator said.

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