Chicago Mayor Rahm Emanuel, left, and challenger Jesus "Chuy" Garcia prepare March 31 for the last televised mayoral debate before the April 7 runoff election. (Charles Rex Arbogast/AP)

“Takin’ Care of Business” was blasting through the loudspeakers inside the banquet hall where supporters were cheering for mayoral hopeful Jesus “Chuy” Garcia. It was his cue to enter. But there was no sign of him.

The DJ had to restart the song. Twice. Then, finally, Garcia arrived.

It was a fitting episode for the firebrand populist underdog who is trying to unseat incumbent Rahm Emanuel in Tuesday’s election. Garcia’s campaign, which has become a rallying point for liberal activists, has been yearning for its breakthrough moment but plagued by false starts.

Perhaps the biggest reason is Emanuel himself. In the nearly six weeks since he was forced into a runoff against Garcia, the mayor has run an aggressive, well-funded campaign that has sought to turn the tables on his upstart challenger. In many ways, the contest has become as much a referendum on Garcia’s qualifications as on Emanuel’s tempestuous first term.

Emanuel “has basically controlled what the runoff has been about,” Democratic strategist Eric Adelstein said. “It’s been about the city having serious fiscal problems and does Garcia have the substance and the plan to get it done.”

The race — polls show Emanuel holding a clear lead — illustrates the serious challenges facing the Democratic Party’s recalcitrant, populist wing as it tries to move the party to the left ahead of the 2016 election. That segment of the party is already struggling to recruit a top liberal alternative to former secretary of state Hillary Rodham Clinton, who is expected to launch a presidential run.

The Chicago campaign shows how the governing wing of the party stands ready to forcefully reject the idea it is insufficiently progressive, explain why controversial decisions were necessary and call out less-seasoned challengers.

“Who is better to steer this ship and right this ship financially, educationally and continue to make the critical investments?” Emanuel asked in an interview with The Washington Post. “That’s the question. And that’s what people have to decide.”

Emanuel, a former congressman and President Obama’s first White House chief of staff, has been battling a backlash against his first-term agenda. He has faced intense criticism over education — he shut down 49 elementary schools to close a budget shortfall; violent crime — the latest quarterly report showed an uptick in homicides and shootings from a year ago; and the city’s fiscal health — Moody’s recently downgraded the city’s debt rating.

Garcia, a Cook County commissioner with a signature mustache, has sought to use those issues, along with Emanuel’s backing from wealthy donors, to argue that the mayor has prioritized the needs of the affluent at the expense of everyone else.

“People in Chicago are dissatisfied with the type of politics its leader has practiced — essentially catering to the rich and powerful interests,” Garcia, who would be the city’s first Mexican American mayor, said in an interview with The Post.

But in the runoff, which was triggered when Emanuel led but failed to win a majority in the Feb. 24 election, Garcia has also dealt with mounting questions about his executive résumé and what his critics say is a glaring lack of specifics in his platform.

Emanuel and his allies have pummeled Garcia with TV ads charging that the challenger hasn’t adequately explained how he will pay for the spending he is proposing and could raise taxes.

The mayor has also called Garcia’s leadership of a nonprofit organization into question. In the final televised debate, Emanuel held up a tax form showing that the group ran a deficit and hit Garcia for overestimating its operating budget. Garcia retorted that organization is in “solid financial health.”

The millions of dollars in attack ads have taken a toll on Garcia. “What you have in effect is Rahm, with serious money, has just awakened his people,” said Paul Green, a political scientist at Roosevelt University in Chicago.

Overall, Emanuel has raised about $20 million for his reelection bid, while Garcia has raised about $4 million for his campaign. The mayor has received a substantial cash infusion in the runoff from billionaire hedge fund manager Ken Griffin, who has also donated to Republican candidates.

“The big money interests in Chicago hijacked our government. They’re running scared,” Garcia said at the Wednesday rally with city workers at the banquet hall.

Sen. Bernard Sanders (I-Vt.), who is considering running for president with an emphasis on fighting income inequality, campaigned for Garcia on Thursday night. “I need a Chuy button for Sanders!” an organizer said just minutes before the senator took the stage.

In an interview before the event, Sanders said he was not there to “campaign against” Emanuel, whom he has known “for many, many years,” but rather to stump “for Chuy.”

The Vermont liberal, who expressed concern about Emanuel’s ties to wealthy donors, said the country needs “a political revolution.” He acknowledged that it will not be easy and that his political future remains undecided.

“It’s not easy stuff,” he said. “People are demoralized. Many people have given up on the political process.”

Many liberals want to see Sen. Elizabeth Warren (D-Mass.), the country’s most prominent liberal politician, challenge Clinton, the presumed early front-runner for the Democratic nomination. But Warren has repeatedly said she does not plan to do so.

Without Warren, the populist mantle will likely be left to Sanders or former Maryland governor Martin O’Malley. Like Sanders, O’Malley is weighing a run and would face very long odds against Clinton.

In Chicago, Emanuel has met criticism that he has veered too far to the right and is too cozy with moneyed interests head-on, vigorously defending his liberal credentials. In the interview, he emphasized his minimum-wage increase, expansion of early-childhood education and the drop in the annual homicide rate during his term.

“It’s a progressive agenda,” he declared.

In addition to defending his policies, the famously irascible mayor has tried to soften his image. He released a direct-to-camera TV ad this past week in which he says: “Chicago’s a great city. But we can be even better. And yeah, I hear you, so can I.” In an earlier runoff ad, he acknowledged that he can “rub people the wrong way, or talk when I should listen.”

When he went to cast his ballot Thursday during early voting, Emanuel was in the mood for cracking jokes.

“Sorry to bring you all my family with me,” he kidded to the poll workers, referring to the pack of reporters following him.

Fielding questions from reporters afterward, Emanuel noted that this is the first election in which his son, Zach, is eligible to vote.

“We’re still working on him. He’s undecided,” he quipped.

A Chicago Tribune poll released this past week showed Emanuel with a commanding 28-point lead over Garcia. But both sides say they don’t think the race is that lopsided.

It’s unclear whether high turnout in early voting, which ended Saturday, will continue Tuesday, amid external factors that could affect the unprecedented election.

“We’re heading into spring break. There’s two days after Easter. It’s right in the middle of Passover. I mean, we’ve never had a runoff before in the city of Chicago for a citywide office,” Election Board spokesman Jim Allen told reporters.

At the Sanders rally, Karen Lewis, the teachers union head whom many expected to challenge Emanuel — she declined after falling ill with a brain tumor — framed the stakes of the election: “This has got to be the start of a movement. This can’t be about one election, one election cycle.”

Lewis, who has clashed with Emanuel, added: “We have sat around a long time waiting for a savior, which I don’t think anybody’s sending. But we have to have little ones all over the place all the time.”

To hear the mayor tell it, whatever happens Tuesday shouldn’t be over-read outside the city limits.

“Trust me, 99.9 percent of people are voting to cast a ballot for the future of Chicago, not the future of the Democratic Party,” he said.