Chicago Mayor Rahm Emanuel talks to reporters after a mayoral debate on Jan. 27. (Al Podgorski/AP)

The crowd at the Irish American Heritage Center was subdued, some quietly sipping beers. The moderator reminded mayoral hopeful Jesus “Chuy” Garcia that the incumbent, Rahm Emanuel, had a much bigger campaign war chest.

“And more fear of me than I of him,” Garcia, a mustached Mexican American upstart, snapped back, and the audience was subdued no more.

President Obama returned to his home town Thursday, where he sought to propel Emanuel, his former chief of staff, to a second term. The race remains surprisingly competitive, and it has crystallized some of the deep internal divisions in the Democratic Party as it prepares for the 2016 presidential campaign.

Garcia has emerged as a nothing-to-lose dissenting liberal voice who has channeled frustration with Emanuel’s rocky first term into an aggressive campaign against the mayor. The Chicago fight has become the latest front in a simmering nationwide battle between the establishment governing wing of the Democratic Party and a more restive, populist wing that is demanding a more openly liberal agenda.

Garcia, a Cook County commissioner, has picked up the torch of the economic populist movement embodied by Sen. Elizabeth Warren (D-Mass.) and New York Mayor Bill de Blasio. Emanuel is being cast as part of the establishment that includes Obama and Hillary Rodham Clinton and has been accused of being too cozy with Wall Street and big banks at the expense of average Americans.

Candidates for the office of Mayor of Chicago from left to right, Mayor Rahm Emanuel, businessman Willie Wilson, Alderman Bob Fioretti and Cook County Commissioner Jesus Garcia look on before a televised debate at WTTW in Chicago, Wednesday, Feb. 4, 2015. The candidates are vying for mayor in the Feb. 24, election. (Nam Y. Huh/AP)

There’s little doubt that Emanuel will finish well ahead of Garcia and three other challengers in Tuesday’s election. But polls show him at risk of falling short of a majority and being forced into a six-week runoff campaign, probably against Garcia. Liberal activists are relishing the opportunity to extend the race.

“I think the broader context is a continuation of what we saw with Bill de Blasio’s win in New York a year ago,” said Ilya Sheyman, executive director of the liberal group Political Action, which has dispatched a full-time organizer to help Garcia and is raising money for him. “All across the country, particularly in cities, we’re seeing that the progressive economic populist agenda is gaining steam.”

In his campaign literature, Garcia has called Emanuel “Mayor 1 %” while declaring himself a potential “mayor for all of us.” He has attacked Emanuel’s record on education, crime and wages, in an effort to brand him as being more devoted to the city’s wealthier residents than its working-class and poor constituents.

“The city center is doing well; however, the city center comprises only 1 percent of the city landmass. Thus the question: What about the rest of the 99 percent of the neighborhoods?” Garcia asked the mostly white crowd at the Irish American Heritage Center, which held a candidate forum Monday night.

Emanuel, a former North Side congressman and Obama’s first White House chief, was elected in an open 2011 race to succeed Richard M. Daley, who was mayor for more than two decades. Emanuel is promising to build on the policy changes he has made over the past four years, such as increasing the minimum wage, expanding full-day kindergarten and attracting businesses to the city.

“We’re going to continue to make investments throughout the city of Chicago in all parts of the city,” Emanuel told reporters Wednesday.

But Garcia is pushing an even higher minimum wage. Backed by the Chicago Teachers Union, which has clashed sharply with Emanuel, most notably in a 2012 strike, he has blasted the mayor’s controversial decision to shutter nearly 50 elementary schools to close a budget deficit. And he wants to replace the city’s appointed school board with an elected one.

Garcia, who was born in Mexico, is an unlikely standard-bearer. He jumped into the race in the fall only after the teachers union leader, Karen Lewis, who was widely expected to run, opted not to because she has a brain tumor.

Although Garcia has been focused on Emanuel, he also has criticized Obama, saying the president hasn’t delivered on income inequality and other economic concerns.

“It’s disappointing,” Garcia told The Washington Post in an interview between campaign stops Tuesday. “I don’t think that he has signaled a clear direction or demonstrated enough empathy for how much people have suffered.”

Hopping out of a sport-utility vehicle during a snow flurry, Garcia expressed similar concerns about Clinton, the presumed Democratic presidential front-runner. But he said that Warren, whom MoveOn and other liberal groups are trying to coax into a White House run, “has been more forthcoming” on those issues.

Clinton and Warren are not involved in the mayoral race. But Obama is, as Emanuel’s highest-profile backer. He has done a radio ad and designated the historic Pullman Park district as a national monument during his Thursday trip.

Pullman Park was the birthplace of the first African American labor union in the United States, and the timing of the president’s trip could be a boost for Emanuel, particularly among black voters. The mayor won every majority-black ward in the city in 2011 and is heavily courting black voters again.

Emanuel introduced Obama at the dedication, and the president later stopped by an Emanuel campaign office. In his remarks, the president praised Emanuel as a key part of his White House staff. “Now, before Rahm was a big-shot mayor, he was an essential part of my team at the White House during some very hard times for America,” Obama said.

And the president went on to say that Emanuel is a fighter for Chicago: “Rahm hasn’t just fought for a national park in Pullman, he’s fought for new opportunity and new jobs in Pullman, and for every Chicagoan, in every neighborhood, making sure every single person gets the fair shot at success that they deserve.”

Earlier, speaking at a heavily African American retirement community on the South Side on Wednesday, a hoarse Emanuel quipped, “This is the wear and tear of telling my wife I love her so many times on Valentine’s Day.” Before having lunch with the residents, he told them he knew there were “a lot of grandparents” in his audience.

“The next four years are not about the next four years,” he said. “The next four years are about the next generation, and making sure our kids are on the right track to do the right things.”

Garcia also is competing hard for black voters. He has touted his close ties to the late Harold Washington, the city’s first black mayor. Garcia was Washington’s deputy water commissioner and remained a close ally as an alderman.

He also has raised concerns about crime under Emanuel’s watch, decrying “10,000 shootings in the last four years” in a TV ad.

Still, according to a Chicago Tribune poll released this week, Garcia is carrying only 13 percent of the black vote.

Ensuring strong turnout among Hispanic voters is a key component of Garcia’s strategy. He spent Tuesday afternoon canvassing taquerias in Little Village, the Mexican American enclave where he grew up, making his pitch in Spanish and English, posing for selfies with supporters, and making small talk with the lunchtime crowd.

Garcia is facing is a sizable fundraising disparity. Emanuel started the year with nearly $6.5 million in his campaign account, allowing him to blanket the airwaves with ads. Garcia, who is using a former restaurant as his campaign headquarters, had about $818,000 on hand.

So Garcia has been relying on his mustache, which has taken on a life of its own, and his nickname, Chuy, a Mexican moniker for Jesus, to sharpen his public profile without dishing out the money normally required to boost name recognition.

His supporters sport campaign buttons with a mustache logo and signs bearing his nickname. He even has encouraged backers to tweet a hashtag referring to his facial hair.

“Don’t blame me, I just haven’t shaved since I was 14,” he joked.

Garcia’s charm offensive, critics say, masks a platform that is short on specifics. At a news conference on education Tuesday, he made an imprecise pitch to shrink school class sizes.

Speaking about Emanuel’s opponents, Rep. Luis V. Gutierrez (D-Ill.), an Emanuel convert who didn’t back him in 2011, said, “They are very articulate about what they dislike about Rahm. But they are very scarce on plans for the future of the city of Chicago and most important, how you’re going to pay for it.”

Despite the head winds, the Tribune poll showed that Garcia has remained in contention for the runoff in the final days, and he appears to have separated himself from three other challengers: Alderman Bob Fioretti, businessman Willie Wilson and perennial contender William “Dock” Walls.

In another sign that Garcia’s populist push has made him a real factor, Emanuel launched a recent TV ad portraying him as a tax-raiser who voted to increase his own pay.

Because Daley coasted to reelection for so long, many voters are unaccustomed to this level of competition involving a sitting mayor.

“Everything in Chicago has been preordained,” said Marty Castro, a lawyer who is backing Garcia. “Not this time.”