(CNN) Republican Sen. Cindy Hyde-Smith of Mississippi accused Democrats at a debate Tuesday night of weaponizing her recent remark about attending a "public hanging" at the invitation of a local rancher.

The comment, which was captured on tape and quickly went viral, called up dark memories of lynchings in the state. Asked about it by a moderator, Hyde-Smith said she would "certainly apologize" to anyone who was offended, but then pivoted to an attack on her opponent, Democrat Mike Espy, a former congressman and US agriculture secretary running to become the state's first African-American senator since Reconstruction.

"I also recognize that this comment was twisted and it was turned into a weapon to be used against me," Hyde-Smith said. "A political weapon used for nothing but personal and political gain by my opponent. That's the type of politics Mississippians are sick and tired of."

Hyde-Smith set off the furor earlier this month when, at a campaign event in Tupelo, she used what her campaign has since dismissed in a statement as "an exaggerated expression of regard."

"If he invited me to a public hanging," she said of the man, "I'd be on the front row."

On Tuesday, inside a small television studio with no live audience, Espy rejected Hyde-Smith's claim that her words had been taken out of context.

"I don't know what's in your heart, but we all know what came out of your mouth," Espy said, before channeling the message he put out in an ad earlier in the day. "It's caused our state harm. It's given our state another black eye that we don't need. It's just rejuvenated old stereotypes that we don't need anymore."

Hyde-Smith and Espy will face off next week, on November 27, in a runoff for the Mississippi US Senate seat she was appointed to earlier this year.

Given the chance to rebut Espy, Hyde-Smith repeated her earlier response almost to the word, saying, "My comments were taken and twisted and used as a political weapon against me by my opponent. That is just wrong. It is unfortunate, and that's the type of politics Mississipians are tired of."

Hyde-Smith's "public hanging" riff and a subsequent tape, which showed her joking -- as her campaign put it -- about suppressing the votes of students at liberal colleges, have triggered a backlash among Democrats nationwide and more recently from large corporations like Walmart, which on Tuesday withdrew its support for her campaign and asked for its donations to be returned.

A recent filing with the Federal Election Commission showed Walmart had given Hyde-Smith's campaign $2,000.

"Sen. Hyde-Smith's recent (hanging) comments clearly do not reflect the values of our company and associates," Walmart said on Twitter. "As a result, we are withdrawing our support and requesting a refund of all campaign donations."

Google, which gave Hyde-Smith $5,000, backed away from the freshman senator last week.

"This contribution was made on Nov. 2 before Sen. Hyde-Smith's (hanging) remarks became public on Nov. 11," the company said in a statement. "While we support candidates who promote pro-growth policies for business and technology, we do not condone these remarks and would have not made such a contribution had we known about them."

Union Pacific and Boston Scientific also defended their initial decisions to give, saying on social media that they had made their donations before the "public hanging" video become public, but requested that they be returned.

It is not clear whether Hyde-Smith has agreed to recoup the donations. Her campaign did not immediately respond to a request for comment.

On Monday, Hyde-Smith returned a $2,700 donation from a Seattle businessman, Peter Zieve, whose company, Electroimpact, was sued by Washington state for discriminating against Muslims.

But the comment that first got the country's attention took place at a campaign event alongside a cattle rancher she described on Tuesday as "a supporter who has a big piece of my heart."

On Tuesday night, she compared the "hanging" comment to another she had made about the same person, saying, "To express my deep regard for and my sincere commitment to this young man, I used a phrase: I told him would fight a circle saw off for him."

"Well, obviously I would not stick my arm in a circle saw," she said, explaining her rhetorical exaggeration and comparing it to her comment about public hanging. "Nor did any of my comments ever mean I would enjoy any type of capital punishment sitting there witnessing this."

In a new ad released Tuesday, Espy warned Mississippi voters -- much as he did during their debate -- that electing Hyde-Smith would reinforce "the stereotypes that hurt our state."

"We can't afford a senator who embarrasses us and reinforces the stereotypes we've worked so hard to overcome," a narrators says. "We're better than this, Mississippi -- and that's no joke."

Democratic Sens. Cory Booker of New Jersey and Kamala Harris of California have campaigned for Espy in Mississippi in recent days. On Monday, former Vice President Joe Biden announced his endorsement of Espy, while others, like Sen. Elizabeth Warren of Massachusetts, have sent out fundraising emails.

Hyde-Smith, whose Mississippi colleague Sen. Roger Wicker won re-election earlier this month by nearly 20 percentage points, has run into an assortment of self-made roadblocks during the runoff campaign.

Photographs from 2014 of Hyde-Smith posing with Confederate artifacts also surfaced on Tuesday, another headache for her campaign a week out from the runoff election.

She posted one image with a caption -- "Mississippi history at its best!" -- after touring the home and library of Confederate President Jefferson Davis. In the same post, Hyde-Smith appears in four additional photos with Confederate rifles, soldiers' hats and documents.

Some Democrats believe Espy is now within striking distance of flipping a Senate seat in a state that President Donald Trump won by nearly 20 percentage points in 2016. Trump is scheduled to lead a pair of rallies, in Biloxi and Tupelo, for Hyde-Smith on the day before the election.

Hyde-Smith began the debate by plugging Trump's planned appearances, using her opening statement to thank him for coming.

"The President of the United States is coming to Mississippi to campaign on my behalf," she said before ticking off the dates, times and locations of his rallies.

Espy, following the lead of other successful Democrats in 2018, pledged to cut an independent figure in Washington if elected and he attacked the state's Republican leadership for turning down Medicaid expansion funding under Obamacare.

"That's why now we have all these rural hospitals in Mississippi closing," he said, "because we did not accept the Medicaid expansion money and we have uncompensated care."