Candidates Joe Sestak and Katie McGinty during the U.S. Senate Democratic Primary Debate in University Park, Pa. (Abby Drey/Centre Daily Times via AP)

Katie McGinty has never been elected to anything, and her name is not well known to Pennsylvania voters. So last week, at a bustling transit stop in West Philadelphia, the unlikely Democratic candidate for the U.S. Senate was relying on a local power broker to sell her to his skeptical constituents.

A friend with a bullhorn beckoned commuters as state Sen. Vincent Hughes (D) insisted that McGinty would prevail in Tuesday’s Democratic primary on the strength of endorsements from powerful party leaders, including President Obama.

“There’s a crystallization, largely in the African American community, around Katie as they see folks like myself and others come out in support of her,” Hughes said.

Although much attention has focused on the divisive Republican presidential primary, Pennsylvania demonstrates that in some key Senate races, Democrats are struggling to capi­tal­ize on the chaos in the GOP. In the race to oust Republican Sen. Patrick J. Toomey, McGinty will face off Tuesday against the better-known Joe Sestak, a retired three-star admiral and former congressman whose go-it-alone approach to politics has alienated the entire Democratic establishment.

Democrats are also in conflict in Florida, where Rep. Alan Grayson is challenging Rep. Patrick Murphy for a shot at the seat being vacated by failed GOP presidential candidate Marco Rubio — another must-win race for Democrats trying to reclaim the Senate.

In both races, Obama and Vice President Biden have abandoned their past reluctance to engage in primary politics. They announced their support for Murphy and dispatched Biden to campaign for him — just as they are sending the vice president to Philadelphia on Monday for a second trip to boost McGinty.

If Democrats win the White House and gain four seats in the Senate, they would regain the majority they lost in 2014. Obama and Biden, both former senators, have made it a personal goal to help return the Senate to Democrats’ control before they leave the White House in January, even if it means ruffling feathers in the party’s progressive wing.

In Pennsylvania, the feud is more about personality than policy: Democratic leaders despise Sestak, who never stopped campaigning for the Senate after losing narrowly to Toomey six years ago.

“I don’t think anybody would call Joe Sestak paranoid if he said the Democratic Party was out to get him,” said John Fetterman, the mayor of Braddock and the third Democrat in the race.

The dispute has turned into a roughly $10 million brawl for the nomination that is likely to leave the victor broke and in desperate need of a strategy to unify the Democratic ranks against Toomey and his $10 million campaign war chest.

Polls showed Sestak, 64, with a large early lead. Now the race is neck and neck, but no one is sure whether McGinty, 52, can marshal her momentum and financial edge to overcome the reservoir of goodwill that Sestak has established during his years-long, nonstop campaign.

“The congressman, God bless him, has been running for a long, long time, and so we didn’t have the name ID advantage to start with,” McGinty said after meeting with a dozen senior citizens in Center City. “But I think every poll is showing that we have eviscerated that early lead.”

The ninth of 10 children from an Irish Catholic family in Northeast Philadelphia, McGinty attended St. Joseph’s University and now lives in the suburbs. She served as an environmental adviser to former vice president Al Gore and former Pennsylvania governor Ed Rendell (D), and last year served as chief of staff to Gov. Tom Wolf (D).

But McGinty has run in just one previous race, finishing a distant fourth in the 2014 Democratic gubernatorial primary. Her commercials tend to feature others talking about her — in one recent ad, Obama’s voice made up almost the entire audio — rather than the candidate explaining her policy proposals in her own voice.

McGinty has been willing to throw elbows. She has accused Sestak of contemplating cuts to Social Security benefits, because he once said nice things about a bipartisan debt-reduction plan known as Bowles-Simpson. And she has twisted his 2009 vote in favor of a proposal to tax Wall Street bonuses into an allegation that he supports unlimited bonuses for bank executives.

Still, it’s a measure of their deep dislike for Sestak that party leaders are backing such an unproven candidate in such a critical race.

In addition to helping McGinty’s campaign raise money, Democratic leaders have helped build an outside coalition of support that includes the Democratic Senatorial Campaign Committee, Emily’s List, labor unions and environmental groups. All told, the outside groups have so far spent an additional $4 million on McGinty’s behalf.

“This has become a campaign that is driven by Washington, D.C.,” Sestak said in an interview with The Washington Post.

For his part, Sestak says he tried to mend fences with party leaders. He says he considered their recommendations for his new campaign manager and fundraising chief. But he says he just couldn’t take it when he was given a direct order by a senior Democrat: “Sestak, whenever I tell you anything, the only answer is yes.”

In the interview, Sestak declined to name the party boss in question, but in earlier talks with local media, he made clear that it was Sen. Charles E. Schumer (D-N.Y.).

Schumer declined to comment, but a spokesman said the exchange did not occur as Sestak described it. Several Democrats in Washington confirmed that Sestak and Democratic leaders clashed over staffing issues, but they said the decision to oppose Sestak was ultimately based on the belief that a liberal woman could mount a better challenge to Toomey in a year when the Democratic presidential nominee is likely to be Hillary Clinton.

In theory, Sestak should be a dream candidate: He hails from the vote-rich suburbs of Philadelphia. He graduated from the U.S. Naval Academy and received a PhD from Harvard’s Kennedy School of Government. He was a national security adviser to former president Bill Clinton, and he went on to command a carrier group in the early days of the war in Afghanistan. He returned to Delaware County, west of Philadelphia, in 2006 and won a House seat that had long been in Republican hands.

Then in 2009, Biden and then-governor Rendell persuaded one of Pennsylvania’s sitting U.S. senators, Arlen Specter, to switch from the Republican Party to the Democratic Party, giving Democrats a filibuster-proof 60-vote majority in the Senate. That decision permitted Obama to pass major legislation during the first two years of his administration, but it left Specter badly weakened back home.

Smelling blood, Sestak bucked party leaders and defeated Specter in the 2010 Democratic primary. He lost the general election to Toomey by just 2 percent.

Over the next four years, Sestak attended more than 800 events for local Democrats to sustain support for another Senate run. But Sestak likes talking to township commissioners far more than Democratic power brokers in Washington and Harrisburg, the state capital.

“I’ve not heard from him in more than six years,” Hughes said at the street-corner event in West Philadelphia. “You’ve got to reach out to people, and if you want to know what the folks in this community are thinking about, you should talk to the individuals who represent them.”

In an email to supporters that was leaked to a liberal blog, Sestak said that Philadelphia Democrats such as Hughes and Rep. Robert A. Brady (D-Pa.) have never forgiven him for refusing to put up $500,000 in “street money” to get voters to the polls in 2010.

Once McGinty entered the race, Sestak gave up trying to mend his tattered ties to Democratic leaders. Instead, he has once again pursued a highly idiosyncratic campaign strategy, one that includes, in the campaign’s final week, the decision to do very few public events.

In a game plan he crafted himself, Sestak is letting his TV and radio ads do the talking while he holds private meetings with grass-roots leaders. He says running a campaign his way is more important than winning.

“Trust is the biggest deficit we have today,” Sestak told The Post. “This isn’t about my being elected. This is about earning the trust of the people.”