GOP candidates on why party keeps losing, Tim Scott exits race and more takeaways you may have missed

Some of the major Republican candidates not named Trump saw an opportunity in their party's poor election performances last week: Blame the former president, their biggest rival in the 2024 race.

Elsewhere on the trail, Joe Biden sought to build some reelection buzz in South Carolina and Tim Scott brought his girlfriend, briefly, into the spotlight -- and then promptly ended his White House bid.

Here are the campaign updates you may have missed.

GOP primary candidates weigh in on abortion, Tuesday's results

Tuesday's elections proved largely dismal for Republicans, continuing an off-year trend for conservatives since the Supreme Court struck down the abortion protections of Roe v. Wade. As Democrats won big in Kentucky, New Jersey, Ohio, Pennsylvania and Virginia, the Republican candidates for president sought to explain why.

For a few of them, there was one answer.

Former South Carolina Gov. Nikki Haley was frank in her assessment. Her campaign released a memo on Wednesday that rattled off the defeats and then concluded, in part: "Trump is a loser."

Unsurprisingly, former New Jersey Gov. Chris Christie, perhaps the primary's loudest Trump critic, shared this sentiment. He blamed the GOP loss in the Kentucky gubernatorial race solely on Trump, insisting that state Attorney General Daniel Cameron, the GOP candidate, was a "rising star" until he embraced the former president.

"Let's face it, Donald Trump is political and electoral poison down-ballot," Christie said on CNN.

"And the voters of Kentucky -- very red state as you noted -- gave their verdict on politicians who sell their soul to Donald Trump," he said.

Trump, who has long boasted about the power of his endorsement, tried to distance himself from Cameron following the loss to Gov. Andy Beshear.

"Daniel Cameron lost because he couldn't alleviate the stench of Mitch McConnell," he posted on social media, referring to the Senate minority leader, who is not close with Trump.

On the other side of the aisle, Democrats and advocates were saying that abortion rights were fueling Republicans' continued losses. Some GOP candidates agreed, though for a different reason.

Florida Gov. Ron DeSantis said at Wednesday's primary debate that Republicans have not been effectively handling referenda in various states on abortion.

"You've got to be strategic about how you're doing it, know the landscape that you're dealing with," he told NBC News in a post-debate interview. "But they've been getting their clock cleaned on the referenda. I think that's a big problem."

Haley, for her part, has reiterated that she is anti-abortion but has tried to offer what she calls a more pragmatic approach on the issue, acknowledging a federal ban is unlikely to pass Congress and that there should be compromise rather than division between the anti- and pro-abortion access sides.

Minn. Supreme Court dismisses Trump eligibility challenge

On Wednesday, the Minnesota Supreme Court ruled that Trump can remain on the state's primary ballot after his eligibility was challenged under the Constitution's 14th Amendment.

In the ruling, the court wrote: "We reach a different conclusion regarding petitioners' claim that it would be error for the Secretary of State to place former President Trump's name on the ballot for the 2024 general election ballot. That claim is neither ripe, nor is it 'about to occur' as section 204B.44(a) requires."

The former president has harshly criticized the push by some advocates and voters to bar him from the 2024 election because of the 14th Amendment. Supporters of that theory claim he violated Section 3 of the amendment because of his actions around Jan. 6 and in attacking the 2020 election results. He denies all wrongdoing.

Trump's campaign spokesperson, Steven Cheung, released a statement following the court's ruling, calling it "further validation of the Trump Campaign's consistent argument that the 14th Amendment ballot challenges are nothing more than strategic, un-Constitutional attempts to interfere with the election by desperate Democrats who see the writing on the wall: President Trump is dominating the polls and has never been in a stronger position to end the failed Biden presidency next November."

Sen. Tim Scott's mystery girlfriend revealed at GOP debate

Sen. Scott spent part of his presidential campaign fielding questions on his relationship status, given that he was the only unmarried candidate in the race and would have been the first never-married president in nearly 150 years.

In September, he opened up -- a bit -- about the "smart, Christian woman" he has been dating, whom he said was introduced through a friend.

But Scott was also vocal about his reluctance to bringing his girlfriend on the campaign with him. He told The Washington Post in September that he wouldn't want to take her on the trail "unless I have the intention of marrying her."

However, on Wednesday night, immediately following the debate, there she was: Scott's girlfriend, Mindy Noce, appeared alongside him on stage. He said that the two have been dating for about a year.

The relatively silly headlines she made were soon dwarfed by more serious news: On Sunday, in a move that surprised even some of his campaign staffers, Scott said on Fox News that he was leaving the 2024 race. "I think I was called to run. I was not called to win," he said.

The well-liked South Carolina senator had been struggling and he was last in 538's average of national polls among the five people at the Wednesday debate, for which he barely qualified despite his high profile in his party and a significant amount of money raised.

With Scott's exit, there are now four major candidates vying to be the Trump alternative.

VP Harris files for Biden-Harris reelection campaign in South Carolina

On Friday, Vice President Kamala Harris traveled to Columbia, South Carolina, to file on President Biden's behalf for the Democrats' first-in-the nation 2024 primary.

Harris spoke to voters alongside South Carolina Rep. James Clyburn, whose endorsement of Biden in the 2020 Democratic primary is seen as having helped change the course of that race because Biden rallied to win a decisive victory in the state.

In her remarks, Harris emphasized the role of South Carolina in helping choose Biden as the party's nominee the first time and encouraged the state to stick with him. He currently faces two long shot primary challengers, including Minnesota Rep. Dean Phillips, a former member of Democratic leadership, who has vowed to mount a serious run against the president.

"We have momentum. The wind is at our back," Harris told attendees on Friday. "And so let us continue to do what we know how to do. This is a fight for, not against, and it is a fight born out of our sincere and deep love for our country and understanding what is at stake."

The Democratic National Committee previously approved a new primary schedule for this election, making South Carolina the first election in the country -- over New Hampshire, sparking controversy there -- in an effort, officials said, to spotlight parts of the country that are more representative of their diverse base.

ABC News' Gabriella Abdul-Hakim, Libby Cathey, Julia Cherner Abby Cruz, Hannah Demissie, Fritz Farrow, Lalee Ibssa, Nicholas Kerr, Soo Rin Kim, Will McDuffie and Kendall Ross contributed to this report.