HOLLYWOOD, Fla. — She made her way past a man in a coconut-shell bikini top and a burly guy in a parrot-head hat, and then the candidate trying to become Florida's first female governor began swaying to an escapist island tune being played onstage in her honor. Just days before a stubbornly close primary election, the show stood a chance of helping win over an undecided Democratic voter or two.

"What would Jimmy Buffett do?" Jimmy Buffett hollered as he belted out "It's Five O'Clock Somewhere," a testimonial to situations in which it is always happy hour. "I'd vote for her, that's what I'd do!"

The crowd cheered for Gwen Graham, the former Tallahassee congresswoman and senator's daughter seen by national party leaders as a formidable contender to break the Republican Party's 20-year hold on the Florida governor's mansion. A mainstream Democrat, Ms. Graham is a former P.T.A. mom with a golden pedigree who could appeal to the moderate women who have been abandoning the Republican Party since the election of President Trump.

"Help is on the way," she promised the audience.

But this is Florida, where political races, much like Floridians, run a little wild.

The state's primary election on Tuesday [today, August 28] will set up one of the most consequential governor's races in the country in the nation's largest presidential battleground state, which voted twice for President Barack Obama before swinging narrowly to Mr. Trump in 2016. Even though the state has gone blue in some presidential elections, it has not elected a Democratic governor for two decades. Picking one this year would give the party a prominent voice to counter the White House going into the 2020 presidential campaign, and veto power in the next round of redistricting of congressional seats.

Florida takes a measure of civic pride in being a political microcosm of the country, and Democrats here see the governor's race as a testing ground for how to campaign successfully in the Trump era. Should the party try to lure away centrist white voters uneasy with the president, or should it mobilize young and non-white voters who already lean Democratic but often do not vote in midterm elections?

The leading candidates reflect the contours of the national party, and its struggles to decide on its ideological direction. Ms. Graham is the moderate who enjoys the support of national women's groups and argues that it's past time to elect a female governor; Mayor Andrew Gillum of Tallahassee is the outspoken, Bernie Sanders-endorsed progressive who is eager to tug the party toward the undiluted left; and three businessmen — former Mayor Philip Levine of Miami Beach, Jeff Greene, a Palm Beach real-estate investor, and Chris King, an Orlando entrepreneur — are the rich white men, part of an increasingly common breed of wealthy entrepreneurs dipping into their own fortunes to enter the political world.

These familiar battle lines are what have made the unusually tight and unpredictable contest more than a little awkward for the party, and also hard to forecast.

These familiar battle lines are what have made the unusually tight and unpredictable contest more than a little awkward for the party, and also hard to forecast.The campaigns of Mr. Levine and Mr. Greene have dominated the television airwaves. Mr. Gillum, Ms. Graham's friend turned rival, could make history as Florida's first black governor.

Polls suggest Ms. Graham and Mr. Levine are in the lead, with Mr. Gillum gaining ground. Mr. Greene, a billionaire who made a late entry into the race, briefly appeared as a top contender before seeing his popularity wane. Apparently concluding he could not win, he preserved the rest of his fortune by taking his TV ads off the air last week.

Ms. Graham has nicknamed the race "Gwen and the men."

"I'm worried," said Sally Dieguez, 69, a Graham supporter who attended Mr. Buffett's free concert. "Levine and Greene got their ads out very early, and they saturated the TV market."

A few days earlier at the nearby public library, where early voting was underway, Bud Knoop, 62, a retired city gardener, said he "voted for Ms. Gwen" in part as a rejection of Mr. Levine and Mr. Greene, who in attack ads have each likened the other to Mr. Trump.

"I'm tired of the two gentlemen fighting each other, picking on Trump and not saying what they're going to do," Mr. Knoop said.

In a state roiled this year by the mass shooting at Marjory Stoneman Douglas High School in Parkland, dueling toxic algae crises in Lake Okeechobee and the Gulf of Mexico, and the delayed arrest of a white man who shot dead an unarmed black man at a Clearwater gas station, the Democratic candidates have also pledged to push for gun control, adopt robust environmental regulations and try to repeal the controversial self-defense law known as Stand Your Ground. They have also promised to expand health insurance to about 700,000 more Floridians.

Ms. Graham's safe-for-suburbia profile, and a voting record from her single term in Congress that reflects her more conservative Panhandle district, have not exactly been helpful in a primary that has been a race to the left. Democratic leaders in Washington have been frustrated at her inability to lock in a win, irritated at Mr. Levine's self-financed command of the airwaves — especially in expensive South Florida, home to at least a fifth of Democratic primary voters — and Mr. Greene's deluge of attacks. (After spending more than $30 million of his own money, Mr. Greene went mostly off the air.)

"It's hard to run against a multimillionaire and a billionaire," said Stephanie Schriock, who runs the Democratic women's group Emily's List, which will spend more than $2 million for Ms. Graham by the end of the primary. (Ms. Graham is also a multimillionaire.)

Mr. Greene's foray into the race blunted Mr. Levine's momentum and helped Ms. Graham, at least until Mr. Greene started highlighting her family's involvement in a proposed megamall development near the Florida Everglades. Ms. Graham's father, Bob Graham, is a former governor and senator beloved among older Democrats but unknown to many new arrivals.

Mr. Levine, who offers voters an ideological middle ground between Ms. Graham and Mr. Gillum, had campaigned largely on his work as mayor to protect Miami Beach from sea-level rise. He realized quickly that he cut a similar profile to Mr. Greene. Both are self-made Jewish entrepreneurs from South Florida, and voters appeared to confuse them. So Mr. Levine refined his message, comparing Mr. Greene, who until recently was a member of President Trump's elite Mar-a-Lago club, with another wealthy Palm Beach real-estate investor turned politician with no prior government experience.

"We have a president who's in this situation," Mr. Levine said after a recent debate in Palm Beach Gardens. "We are not going to test you on the top job."

Even more delicate in progressive circles is Mr. Gillum's candidacy. Some Democrats were uneasy about rallying to Ms. Graham's side when there was such a promising young African-American in the race. Quashing the aspirations of a viable black candidate for governor would be difficult enough given how reliant the party is on African-American voters in a state where blacks make up 28 percent of registered Democratic voters. But it is an even more sensitive matter with a racially divisive president in the White House. Few in the party were willing to discuss the matter publicly other than to diplomatically emphasize the importance of fielding the candidate most likely to win a state Mr. Trump carried in 2016.

"This race exemplifies how important it is to balance our long-term goals with our short-term, acute need to win in key states," said Ilyse Hogue, who runs Naral-Pro-Choice America, which endorsed Ms. Graham.

In a brief interview this week, Mr. Gillum insisted Democrats should not repeat the same strategy they tried twice unsuccessfully against the Republican governor, Rick Scott: running middle-of-the-road candidates who failed to rally the progressive base and lost each time by about 1 percentage point. This year, Republicans appear likely to choose Representative Ron DeSantis, one of Mr. Trump's most loyal acolytes, as their nominee for governor. He is running against the state agriculture commissioner, Adam Putnam.

"We've got to have a candidate that's able to bring together the diversity of our party in order to win and in order for Senator Nelson to go back to Washington D.C.," Mr. Gillum said, referring to the Democratic incumbent, Bill Nelson, who faces a daunting challenge from Mr. Scott. "I think all of our fates die here. And I believe that me at the top of the ticket, underneath our federal slate, will have the ability to move more voters who don't participate in midterm elections to show up in November."

Quentin James, who runs a group dedicated to electing more African-Americans, echoed Mr. Gillum, saying the "central question" Democrats face is, "Are we going to go after moderate Republicans or seek to revolutionize the election?"

Mr. James's own group, Collective PAC, has helped underwrite Mr. Gillum's campaign, but some Graham supporters believe the organization has taken undisclosed money from Republican-leaning business interests whose intention is to torpedo her candidacy. Mr. James denied Republican involvement, but the group is not required to identify its donors in such cases, and he said two of the entities that had given to Collective did not want to be identified.

Mr. Gillum also got help from the progressive billionaires George Soros and Tom Steyer but struggled to raise money on his own as an F.B.I. corruption investigation loomed over Tallahassee City Hall. He has said he is not the investigation's target, and says his lack of personal wealth is an asset when it comes to relating to regular people.

"He can be a governor for the masses," said Felicia Robinson, a councilwoman in the predominantly black city of Miami Gardens, where schoolteachers at a rally for public education last week greeted Mr. Gillum with excited shrieks, frenzied selfies and the sound of the late Aretha Franklin belting out "Respect" over the loudspeakers.

"I'm sick of losing," Mr. Gillum declared. "I'm sick of losing not because of the names that are on the ballot — I'm sick of losing because of who we lose when we lose these elections: our kids, who are being told they attend failure factories. Our teachers, who are being called failures and evil."

A lightning alarm blared. Mr. Gillum stepped offstage and spotted a woman dressed in her Sunday best, sitting in a folding chair under the shade of a tree. She was Ms. Robinson's mother, Carletha Robinson, 80. Mr. Gillum gave her a high-five.

"Let's make history right here, together," he said.

Behind him, though, was the candidate who had won the endorsement of the statewide teachers' union. She took the microphone. It was Ms. Graham.

TThe New York Times, August 27, 2018

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August 28, 2018

Post Script. The article above makes clear many issues of Today’s Florida’s Democratic Primary [Tuesday, August 28]. But let’s lay out what is crucial here. Democrats, get out the vote to pick your candidate - whether Gwen Graham, Andrew Gillum, Philip Levineor Jeff Greene. I myself would pick Graham, as did Emily’s List, but whoever you want. Vote and GOTV. #FloridaPrimary2018 #RunUptoMidterms2018

FYI, Last week’s Sun Sentinel Poll shows Gwen Graham at 29 percent — well ahead of competition in Democratic primary for governor.