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NEW YORK (CBS News) --New York City's wild mayoral primary campaign landed in the voting booth Tuesday as New Yorkers began the process of replacing the man who has defined their city for 12 years.

Mayor Michael Bloomberg never offered an endorsement in the race, but the campaign has been defined by his legacy. The Republican mayoral hopefuls in Tuesday's election are largely promising to maintain his policies, while the Democrats have offered a sharply different approach.

Their front-runner, public advocate Bill de Blasio, is pitching himself as the cleanest break with the current administration. And while just weeks ago his campaign was an afterthought, he now has a legitimate shot of surging right past the 40 percent mark that would enable him to avoid a runoff three weeks from now.

In a Quinnipiac University poll released Monday, de Blasio was the choice of 39 percent of likely Democratic voters. If no one reaches 40 percent, the top two finishers advance to an Oct. 1 runoff.

De Blasio's rise was as sudden as it was unexpected. He benefited from placing his interracial family at the heart of his campaign, connecting with voters over the need for NYPD reforms, and by drawing away voters wholeft Anthony Weinerfollowing the former congressman's latest sexting scandal.

If de Blasio's support holds, the other spot in the potential runoff appears to be a battle between City Council Speaker Christine Quinn and former comptroller Bill Thompson.

Quinn, who is bidding to become the city's first female and first openly gay mayor, led the polls for most of the year but has seen support disappear as her rivals have repeatedly linked her to the bitter debate to let Bloomberg run for a third term in 2009.

The mayor's opponent that year was Thompson, who stunned the political world by nearly upsetting the billionaire incumbent. The race's lone African-American, Thompson has said he is counting on winning the bulk of black and Latino voters to propel him to the runoff.

Election experts estimate that minority voters will make up more than half the Democratic primary electorate. Most polls have Quinn and Thompson within a few points of each other.

Weiner jolted the race in May when he ended his self-imposed political exile that began when he resigned from Congress in 2011 after sending lewd online messages to women who were not his wife. He led the polls for nearly a month only to tumble when it was revealed that he had continued to send the explicit messages in the months after leaving office.

The comptroller, John Liu, is bidding to become the city's first Asian-American mayor but has been dogged by a fundraising scandal. He has been polling in the single digits.

Republicans will look to continue an improbable winning streak. Though outnumbered by Democrats in the city 6-to-1, the GOP has won the last five mayoral elections. (Bloomberg was an independent running on the Republican line four years ago)

Joe Lhota, the former MTA chairman who received acclaim for steering the transit agency through Superstorm Sandy last fall, has led the polls all campaign. A former deputy mayor to Rudolph Giuliani, Lhota has pledged to maintain the city's record low crime rates.

His primary challenger is John Catsimatidis, a billionaire grocery store magnate who has unleashed a series of blistering attack ads on Lhota, including one that mocks the front runner for dismissing Port Authority police officers as "mall cops." Catsimatidis has spent more than $4 million of his own money on the race, but that's a far cry from the $102 million Bloomberg spent four years ago.

Also Tuesday, ex-Gov. Eliot Spitzer will be trying to make a political comeback in the Democratic primary for city comptroller. Seeking to rebuild a political careerdevastated by a prostitution scandal, Spitzer is taking on Scott Stringer, Manhattan's borough president.

Polls showed Spitzer and Stringer in a close race heading into Tuesday. Since Spitzer's abrupt July decision to run, the two have been locked in one of the fiercest political wrestling matches in the city this year.

Seeking a comeback five years after resigning as governor and acknowledging he patronized call girls, Spitzer said Monday he felt the campaign had gotten voters thinking more about his political record than his personal conduct.

"That is out there, but the public has said, 'OK, it's there -- we're judging you based on what you did in government,"' he said on WWRL-AM's "Morning Show with Mark Riley."

Stringer is striving to capture a nomination he once expected to snag easily.

"The job of comptroller has to be watching the backs of people. ... I've been out in the streets. I've been working on these issues" while Spitzer has been out of office, Stringer said in a separate interview Monday on Riley's show.

Spitzer, who was never charged with any crime, has asked voters to focus on his record as a hard-charging governor and state attorney general. He was dubbed "the sheriff of Wall Street" for his financial investigations.

Stringer, a former state assemblyman, says he's mastered both fighting for causes and forging compromises during 20 years in public office.

And he has urged New Yorkers not to forgive or forget his opponent's personal misdeeds.

"I didn't resign in disgrace," Stringer said at a candidate forum last week. Earlier, his campaign sent voters a mailer highlighting Spitzer's involvement with prostitutes and featuring a photo of prison bars.

"If this public wants someone who makes a difference, they know who they're going to vote for," Spitzer responded at the forum, organized by the Council of Urban Professionals, a networking group. Spitzer's aides have sent reporters emails mocking Stringer for proclaiming a Justin Bieber Appreciation Day last year.

Spitzer had double-digit leads in some polls as recently as two weeks ago. But polls Sunday and Monday variously showed the candidates about even or Stringer slightly ahead.

The winner will face a Republican and other opponents Nov. 5.

Experts don't believe turnout will be high Tuesday.

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