Independent candidate for D.C. mayor David A. Catania addresses about 100 supporters who assembled Saturday morning on Pennsylvania Avenue in Northwest. (Aaron C. Davis/The Washington Post)

Independent D.C. Council member David A. Catania launched his bid for mayor eight months ago betting that two things could happen on Election Day that have never happened before.

Catania would have to persuade more than a third of the city’s Democrats to break ranks and vote for someone outside their party. He also would need D.C.’s non-Democrats — one in four registered voters — to turn out in record numbers to support one of their own.

The gambit is about to be tested. On Tuesday, Catania and Carol Schwartz, another independent trailing in third place in public polls, face Democratic council member Muriel E. Bowser. As her party’s nominee, Bowser has seized on decades of Democratic Party dominance in the District to amass an overwhelming advantage in campaign organization and fundraising.

But there remains the uncertainty of a wildly changed city: scandal-weary, no longer majority-black, and eager for school improvements and a closing of the gap between the haves and have-nots, but also largely content with the city’s direction.

And, partisan electoral math notwithstanding, there remains the wild card of who will actually turn out. That uncertainty was on full display Saturday, when Bowser and Catania held competing rallies to kick off a cold and windswept final day of early voting.

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With hugs and high-fives, Bowser worked her way through a crowd of 50 supporters who gathered outside the Takoma Community Center, in her home ward. At the District’s northern tip, Ward 4 is home to some of the city’s most faithful voters in D.C. mayoral contests, and 80 percent are registered Democrats.

Seven miles to the south, Catania, who would be the District’s first non-Democrat, first white and first openly gay mayor, posed for pictures and basked in the applause of over 100 supporters who converged on Pennsylvania Avenue. Voters in the city’s more transient and affluent Ward 2, which stretches across downtown, Dupont Circle and Georgetown, are most likely to be registered as independents, and least likely to vote for Democrats, according to city voting records.

“I’m tired of celebrating the misery of our city,” Catania said as supporters nodded in agreement. “We talk all the time about what we want and we don’t get there. Together, we can make D.C. better.”

Catania’s campaign, centered in part on a promise to continue pushing for public school improvements, has been rooted in a fast-changing political landscape that has given rise to at least some optimism that he could win.

The District is absorbing a wave of new residents who are most often young, white and affluent. Those residents are sticking around long enough to have children, fueling a mini-baby boom that has broadened the number of residents concerned about the trajectory of the city’s enormously costly but so far vastly uneven success at rejuvenating failed city schools.

Catania, a Republican-turned-independent, has walked a tightrope to appeal to all stripes of voters in the District.

To assuage the concerns of Democrats, he has gone out of his way to stress the social and fiscal priorities he shares with the party. He ticks off legislation he has authored over 17 years on the D.C. Council that led to major increases in education spending, expanded access to health care and gay marriage.

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At the same time, Catania has pressed his case with independents, Republicans and even disenchanted Democrats by blasting the city’s ruling Democratic establishment — echoing a sentiment sweeping midterm elections nationally that could propel Republicans to a Senate majority.

And amid a wave of political corruption and skyrocketing income inequality, he has also cast the city’s Democratic leaders as more interested in self-preservation than in protecting the District’s most vulnerable.

Antonio Johnson, 33, who lives east of the Anacostia River and has two children in elementary school and another in diapers, introduced Catania on Saturday morning, saying he believed Catania, and not Bowser, would shake up the status quo.

“It’s the same people involved in her campaign — the same faces, the same money — as all the people elected before her who didn’t put any effort into our side of town,” Johnson said. “I’m saying that, and I’m a Democrat.”

Bowser won the Democratic Party primary in April by positioning herself as the fresh alternative to Mayor Vincent C. Gray, who remains the target of a federal investigation into illicit campaign fundraising during his first mayoral election.

Since then, however, she has cast herself primarily as the candidate of continuity. Bowser has vowed to retain Gray’s chancellor of schools, Kaya Henderson, his police chief, Cathy L. Lanier, and many of his economic policies that have attracted a wave of development and new city revenue.

All of that has given Bowser’s campaign — and the familiar “D” beside her name — the air of incumbency and a natural hook with the seven in 10 voters who in a recent NBC4-Washington Post poll in September said the District is heading in the right direction.

All of that may help explain why, at her rally on Saturday, the feeling was upbeat.

Marvin Bowser, the candidate’s brother, said the biggest challenge would be reminding his sister’s primary-election supporters that there’s a general-election race, too: “There’s some people who say, ‘I already voted for her.’ We’ve got to get people straight on that.”

Bowser’s challenge remains the turnout out of as many Democrats as she can get on Tuesday.

With record-low turnout and a crowded field of competitors, Bowser won the party’s primary in April with 44 percent.

On Tuesday, she will be mathematically unbeatable if, among Democrats, she wins more than 64 percent, according to multiple scenarios acknowledged by Catania’s campaign.

According to he Post poll, which put Bowser ahead by double digits, some of Bowser’s voting base from April has shifted to Catania. But she had also pulled in over half of Democrats who sided in the primary with Gray, who came in second. Yet the poll also revealed a potential weakness for her: two out of three Democrats would “somewhat seriously” consider voting for a non-Democrat.

On Saturday, Schwartz sought to capi­tal­ize on those voters willing to cross party lines by shaking hands and handing out her campaign fliers outside the early voting centers of Hillcrest Recreation Center and Malcolm X Elementary School in Wards 7 and 8. On Sunday, she planned to do the same at the Dupont Circle farmers market, but her campaign planned no more rallies or major events before Election Day.

For Bowser, Saturday was about motivating a group of campaign workers and volunteers to execute a robust get-out-the-vote strategy. She eschewed a megaphone for one-on-one pep talks, but a theme of Democratic unity has suffused her campaign. A mantra since Catania joined the race: “When Democrats vote, Democrats win,” she said.

Catania campaign manager Ben Young contends that all of the conventional wisdom about this year’s mayoral race is flawed, beginning with polls that use past elections to predict dismal turnout among non-Democrats.

D.C. held its primary five months earlier than normal this year to comply with a federal law aimed at giving military members overseas enough time to cast ballots.

The effect was to more than triple the duration of the city’s general election period, giving Catania and Schwartz months, not weeks, to build their case with Democrats and non-Democrats alike.

As Catania raised over $1 million — more than any independent candidate before him — the race also drew in more interest from voters. The race widely became seen as the most competitive since at least 1994, when, damaged by a conviction for cocaine possession, Marion S. Barry defeated Schwartz, then a Republican, by 14 percentage points. It is the closest any Democrat has come to losing a race for D.C. mayor.

A key unknown remaining about Tuesday is just how many independent voters, whose ranks have swelled significantly since 1994, will vote.

In the 2012 presidential race, 53 percent of D.C. voters unaffiliated with either major party cast ballots. In the last mayoral race, the number was just 18 percent.

Among those who contributed to the trend was Anne Filippone, a retired resident of Georgetown. Filippone has almost always voted in national elections. But she said she rarely sees the point in doing so for mayor when it is a fait accompli for Democrats after the primary.

“I’m a little more interested this year, it’s more competitive,” she said. “I plan to vote.”

Add Ward 2 resident Mark Shepanek, NASA’s chief for aerospace medicine, into that category as well. This year, Shepanek said he thinks his vote could mean more.

“It’s slightly frustrating,” Shepanek said. “Previously, my question is always do I wish to connote a landslide for the Democrat, or put in the protest vote to sound the alarm that I would like to have sounded.”

Catania’s campaign has targeted independent voters with mailings, door knocking and phone banking.

“These are people who don’t get touched by campaigns, ever,” Young said. “Nobody is reaching out to independents in the primary, and by the time the general rolls around, Democrats don’t need them.”

Registered independent Moses Saldana, 27, a program analyst at the Treasury Department, said he hadn’t received a call or a piece of mail from any candidate, but his voting location is convenient so he plans to cast a ballot on Tuesday morning.

Like Filippone and Shepanek, however, Saldana said he was still getting used to voting in a local election and figuring out how to research the candidates.

Interviewed on Friday, all three said they remain undecided.

Mike DeBonis contributed to this report.