The Democrats’ dream of winning three gubernatorial mansions in the South during President Trump’s tenure appears possible, though a long-shot, as the races turn toward their homestretch.

The Democrats must take two Deep South states — Louisiana and Mississippi — as well as Kentucky to pull off the trifecta. But even if the GOP were to go down in defeat, some experts cautioned the political situation in each state is so different that the outcomes may not signal much in terms of national trends.

“It’s possible but not likely that Democrats can sweep all of this year’s gubernatorial races,” said veteran political analyst Charlie Cook. “Republicans are underperforming how those states usually vote, but I would be surprised if they lost all of them.”

“These are all three very different local situations and states for the Democrats,” said Ron Faucheux, a former Louisiana elected official who is now a Washington political analyst and consultant. “In Kentucky you have a GOP candidate who is in trouble, and in Louisiana you have a Democrat who is actually pretty popular personally but, from a partisan standpoint, that’s still a risk factor. If the Democrats are going to win two out of three, it will probably be there.”

Mississippi appears to be the Republican bulwark that will hold in November, according to prognosticators, but that is far from certain, and the Democrats have a chance of winning one of the races outright in Louisiana’s Oct. 12 jungle primary.

In Kentucky, Republican incumbent Gov. Matt Bevin is being challenged by Democratic Attorney General Andy Beshear, whose father held the governor’s seat before Mr. Bevin.

Mr. Bevin has an aggressive personal style, but the general landscape in the Bluegrass State is favorable to Republicans.

Reliable polling is scarce, with RealClearPolitics showing just two polls, neither very recent, with one favoring Mr. Beshear by 8 points and the other, from June, giving a 6-point lead to Mr. Bevin. Polls posted by FiveThirtyEight in August show Mr. Beshear with a healthy lead, while the Cook Political Report slots the race as a toss-up.

The Democratic drive to impeach President Trump, which has kicked into overdrive since House Speaker Nancy Pelosi green lighted a formal inquiry into the president’s July 25 phone call during which he pressed the Ukrainian president to investigate former Vice President Joseph R. Biden and his son Hunter, probably will rally Republicans and help Mr. Bevin, many experts predicted.

Mr. Beshear has tried to stay above the fray, although Republicans are trying to pin him down on whether he believes impeachment is appropriate, according to Kentucky media.

“Kentucky is awfully close, but that is more about missteps by Bevin than Trump or the national party,” Mr. Cook told The Washington Times.

In Louisiana, the two main Republican challengers to incumbent Democratic Gov. John Bel Edwards have tried getting him on the record regarding impeachment.

One of them, Baton Rouge businessman Eddie Rispone, who is bankrolling his political debut with $11.5 million of his own money and has made his unwavering support for Mr. Trump his campaign’s main plank, on Wednesday rolled out a video linking Mr. Edwards to congressional Democrats.

Calling impeachment a “witch hunt,” Mr. Rispone said Mr. Edwards backs the Democrats in Congress whether he broadcasts his support or not.

“Liberal John Bel Edwards cannot run from his own party,” Mr. Rispone said. “He was a superdelegate for Barack Obama in 2012 and again for Hillary Clinton in 2016. Liberal John Bel Edwards does not support President Trump, he supports radical leftists like Maxine Waters, Nancy Pelosi and the Squad, and he is going to support whatever lunatic they put up against our president this time.”

Mr. Edwards has tread carefully since Mr. Trump won Louisiana by 18 points. While clearly opposed to much of the president’s agenda, he has not displayed any overt hostility.

“He’s actually been very respectful with Trump,” Mr. Faucheux said. “He’s treated him like the president, not some political enemy.”

That situation began to change when, in a series of Tuesday tweets, Mr. Trump threw his weight behind Mr. Rispone or Republican Rep. Ralph Abraham.

“REPUBLICANS of Louisiana,” Mr. Trump tweeted. “It is really important for you to go out and vote on Oct. 12 for either Eddie Rispone or Ralph Abraham (both Great), which will lead to a runoff against a Nancy Pelosi/Chuck Schumer Democrat (John Bel Edwards) who does nothing but stymie all the things we are doing to Make America Great Again,” Mr. Trump continued. “Don’t be fooled, John Bel Edwards will NEVER be for us.”

Those tweets were followed up by a Saturday fundraising rally hosted by Vice President Mike Pence, and Donald Trump Jr. is scheduled to make a Louisiana appearance Monday on behalf of Republican candidates.

To cap off the flurry of support, Louisiana Republicans announced late Sunday that President Trump would visit Lake Charles on Oct. 11.

All of those developments come at the end of early voting, in which turnout was strong but also reflected an energized Republican base and marginally lower black participation, according to a Sunday blast from Louisiana pollster John Couvillon.

With early voting having started, Mr. Edwards approaches the Oct. 12 primary with a strong lead in the polls, though it is not clear if he will receive the 50% plus 1 of the vote needed to avoid a November runoff against the second-place vote getter.

Early voting is going better for Republicans than expected because Democrats don’t appear energized, according to Mr. Couvillon.

Mr. Edwards has proven unflappable in two debates thus far, saying he turned a state deficit into a surplus and that his policies have Louisiana moving in a positive direction.

“John Bel Edwards has a very good chance of winning without a runoff, that is the best shot for Democrats,” Mr. Cook said. “But that says more about Edwards, the Republican Party in Louisiana and the hangover from Bobby Jindal’s eight years as governor than reflecting on the national party of President Trump.”

The race might not reflect on the Democrats nationally, either, according to Mr. Faucheux.

“You just have very different dynamics in all these races, and the quality of the candidates could have something to do with it all, too,” he said. “So I’m not sure how much any of these three outcomes says about the Democratic Party as a whole.”

Mississippi has a similar scene, although its current governor, Republican Phil Bryant, is term-limited.

On Wednesday, Mr. Trump endorsed Republican Lt. Gov. Tate Reeves.

“Tate is strong on crime, tough on illegal immigration, and will protect your Second Amendment,” Mr. Trump tweeted. “He loves our Military and supports our Vets!”

But recent polls from Hickman Analytics in August and September showed Democratic Attorney General Jim Hood with a narrow lead, albeit within the polls’ margin of error.

That could be partly because Mr. Reeves faced a grueling primary battle against former state Supreme Court chief justice Bill Waller Jr., an establishment Republican, who has declined to endorse Mr. Reeves in the general election.

That raises sour memories for Republicans of infighting that doomed the party’s chances in Louisiana in 2015, when Mr. Edwards rode a fractured opposition to what proved a convincing victory over then-Republican Sen. David Vitter.

It also could have something to do with the retail politicking skills of each candidate, with most analysts giving the edge to Mr. Hood. His ads feature a hunter who drives his pickup truck to work, not a Democrat seething about Mr. Trump.

Still, the Cook Political Report in late September moved the Mississippi race into the “leans Republican” column, partly on the expectation Mr. Trump would stump for Mr. Reeves on the campaign trail, either before or after the race’s only debate Oct. 10.

Mississippi could have one final curve ball in store: a state law from the Jim Crow era that requires the gubernatorial winner to carry not only a majority of the popular vote but also a majority of the 122 state legislative districts, a quirk that could hurt Mr. Hood in a close election.

Republicans hope they can get Mr. Trump to also make appearances in Louisiana should Mr. Edwards be forced into a runoff. The Cook report currently rates it “leans Democratic.”

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