President Trump will jet in next week to campaign with Republican Sen. Cindy Hyde-Smith in Mississippi in the final undecided Senate race, hoping to carry her over the finish line in a race she sometimes seems intent on losing.

Two caught-on-camera remarks by Ms. Hyde-Smith have imperiled what should have been a cruise to the finish line in a runoff set for Nov. 27, in which she faces Democrat Mike Espy, who had been President Clinton’s agriculture secretary.

In one Ms. Hyde-Smith joked about “a public hanging,” and in the other she quipped about voter suppression, putting her on the defensive against Mr. Espy, who is black, and Democrats are hoping the remarks help to increase black voter turnout.

Analysts say it’s unlikely to work.

“In my opinion, Sen. Smith would have to make a far more inflammatory statement or action to dramatically change her level of support statewide; or I suppose a series of them,” said Joseph Weinberg, an associate professor of political science at the University of Southern Mississippi. “I don’t foresee any major ‘surprises’ from either candidate at this point that could swing the vote to any significant degree.”

Ms. Hyde-Smith, a 59-year-old former Democrat, was appointed last year to fill the seat left vacant when longtime Sen. Thad Cochran retired.

She faced voters earlier this month in an election to decide who would fill out the rest of Mr. Cochran’s term, coming in on top 41.5 percent to 40.6 percent for Mr. Espy. Another Republican, Chris McDaniel, claimed 16.5 percent of the vote, and with nobody clearing the 50 percent mark Ms. Hyde-Smith and Mr. Espy moved to a runoff.

In deep red Mississippi, that outcome shouldn’t be in doubt.

And yet Republicans are deploying Mr. Trump to try to shore up Ms. Hyde-Smith, scheduling two rallies for the day before the runoff.

Her first misstep came before a small crowd in Tupelo. Accepting a speaking invitation from someone in the crowd she admired, Ms. Hyde-Smith said she would “be in the front row of a public hanging” if he invited her.

Then, a tape emerged on which Ms. Hyde-Smith, speaking to people at Mississippi State University, joked that perhaps it wouldn’t be a bad thing to make it harder for “liberal folks at those other schools” to vote.

The awkward praise and joke summoned unwelcome memories in a state plagued historically by racism and violence, and Democrats pounced on the chance to call Ms. Hyde-Smith a racist. The American Civil Liberties Union branded Ms. Hyde-Smith’s comments “repugnant,” and Sen. Kamala D. Harris, California Democrat, campaigned in Jackson with Mr. Espy on Saturday, urged voters to show the country Mississippi has changed.

Ms. Harris is just one of the presumed 2020 Democratic presidential hopefuls to hit the trail on Mr. Espy’s behalf. Sen. Cory Booker, New Jersey Democrat, is scheduled to appear in Mississippi on Monday.

But their help could backfire.

“In Mississippi, when you mobilize the left you have to make sure you don’t antagonize another sector,” said Joseph “Dallas” Breen, director of the John C. Stennis Institute of Government at Mississippi State University. “Then there’s the question of how outsiders may influence things; some people in Mississippi are skeptical toward that.”

Ms. Hyde-Smith’s campaign stressed that angle in a statement Sunday afternoon.

“He’s bringing in people like Kamala Harris and Cory Booker to campaign for him, people who will do everything they can to fight President Trump’s agenda,” said Melissa Scallan, a spokeswoman for Ms. Hyde-Smith’s campaign. “All this is doing is showing Mississippi residents that Mike Espy is too liberal to represent their conservative values in Washington.”

On the other hand, Mississippi has the highest percentage of blacks — 37 percent — of any state in the nation. There is also a strain of successful left-wing politicians in Jackson, the capital, and Mr. Weinberg believes, “Sen. Harris is very popular nationally, and so I think this will help Espy quite a bit.”

Mr. Espy has moved carefully in trying to capitalize on Ms. Hyde-Smith’s misstatements, calling them “harmful and hurtful.”

Analysts say a bigger question in the race is what Mr. McDaniel’s supporters do in the runoff. After a year of attacks, he endorsed his former opponent after the election.

“Where do these people go and will the candidates change that 16 percent?” Mr. Breen asked. “That’s the dynamic.”

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