BEAUFORT — One congressional candidate is a former Republican governor seeking redemption after his career imploded in a public saga involving lies, the Appalachian Trail and an Argentine mistress. His Democratic opponent is a famous comedian’s sister who’s trying to benefit from her rival’s damaged reputation.

In a bizarre campaign that has roiled South Carolina, Mark Sanford and Elizabeth Colbert Busch are in a surprisingly contentious contest for a U.S. House seat in a solidly Republican district that GOP presidential nominee Mitt Romney carried by 18 percentage points last year.

Tuesday’s special election is for the seat that Republican Tim Scott held until he was appointed to the Senate. The race has been jumbled by expected low turnout, Sanford’s past and an aggressive late-in-the-game Democratic ad campaign to exploit it.

If Colbert Busch wins, she instantly will become one of the most endangered Democrats in the 2014 elections. If Sanford wins, it could mark a career turnaround.

Early on, Sanford, a third-term congressman before he was governor, appeared to have a significant edge in the district along the Atlantic coast. He beat back primary challengers with an apology-focused campaign and a plea that voters give him a second chance.

But all that changed a few weeks ago with the revelations that his ex-wife had accused him in court documents of trespassing at her home on Super Bowl Sunday.

Sanford disputes that, but has struggled to explain the alleged episode that reminded voters of the 2009 scandal in which he used a story about hiking on the Appalachian Trail to cover up a visit to his then-mistress in Argentina. Sanford avoided impeachment but was censured by the Legislature over state travel expenses he used as part of the affair, and he paid a record ethics fine.

Sanford’s campaign has slid since the trespassing allegations surfaced.

National Republicans, already struggling with a poor showing among women voters in last year’s presidential election, quickly pulled advertising dollars. In doing that, they abandoned the race and made clear that they didn’t think the Republican could recover.

Democrats have tried to take advantage of the moment, sensing an opportunity to gain a seat on GOP turf.

The fundraising arm of House Democrats and Democratic-leaning outside groups aired TV ads assailing Sanford for betraying their trust. After initially declining to make Sanford’s dalliance an issue, Colbert Busch changed course last week, telling voters during a televised debate that Sanford used taxpayer money to “leave the country for personal purpose.”

Sanford’s past has generated more than your run-of-the-mill political interest.

A website that promotes adulterous affairs slapped Sanford’s image on a highway billboard outside the district, urging people to seek their own “running mate.” Hustler magazine publisher Larry Flynt endorsed Sanford, calling him “America’s great sex pioneer.” Flynt later complained when the ex-governor refused to accept the endorsement or a $2,600 donation.

South Carolina Republicans are worried.