Shrugging off a Chicago Sun-Times poll that shows his popularity plummeting, Mayor Rahm Emanuel said Wednesday he ran for mayor on a promise to confront vexing problems “swept under the rug” and he’s not about to “blow with the wind.”

 “There’s ups and downs. . . . You stay true to your principles. You stay true to who you are and you don’t change. You stay committed to making sure there’s results and you stay true to what you believe in,” Emanuel said.

“I’ve been in politics long enough. . . .People go up. People go down. My job is to stay focused on delivering results for people and taking on the challenges the city faces. . . .The moment you decide that you’re gonna blow with the wind, folks are smart and they’ll smell it.”

Emanuel cited a few examples of the tough challenges that may have cost him politically.

The longer school day, the five-month closing of the CTA’s Red Line South and his proposal to save the Municipal Employees and Laborers pension fund by raising employee contributions by 29 percent, reducing employee benefits and requiring reluctant Chicago aldermen to raise property taxes by $250 million.

“We had to do what we had to do — the tough things and spend the political capital to make sure people were getting better results,” he said.

“I would not back down because I would not be a politician or a public servant [who] said, `You know what? I’ll say it when I run for office, but when I get here, `Ooh. That’s hard. Forget about it.’ I’m not throwing the towel in on the kids of the city of Chicago.”

With only 29 percent support from likely voters and eight percent among African-Americans who helped put him in office, there’s a growing perception that Emanuel is in trouble as he prepares to launch his re-election bid.

The Sun-Times poll — and County Board President Toni Preckwinkle’s 26 percent showing among all voters and 40 percent among blacks — is likely to rachet up the pressure on Preckwinkle to challenge Emanuel.

That’s even though Emanuel is raising campaign cash at a frenzied pace — with more than $7.4 million in the bank already and former President Bill Clinton headlining a mega-fundraiser next month — in hopes of scaring off serious challengers.

The mayor is looking so politically vulnerable these days, the fashion police were even after him on Twitter for wearing a denim workshirt over a Blackhawks T-shirt at Sunday night’s game at the United Center.

On Wednesday, Emanuel saw that criticism as an opening to soften his image by portraying himself as the doting father that voters seldom see. 

“I have a 15-year-old daughter. She asked, ‘Dad, can you take me to a hockey game?’ If your daughter at 15 still wants to be seen with you, don’t worry about how I’m dressed,” the mayor said.

“I wore a Blackhawks T-shirt. . . . If she doesn’t’ think wearing a blue jean denim shirt is a problem for her, [then nobody else should, either]. . . . I’m so happy my daughter wants to be with her father. If all you’ve got is someone else to comment on me and what I wear, you’ve got too much time on your hands. . . . I’m not embarassed. . . . You’ve got other things you can worry about. Don’t worry about me and how I dress at a Blackhawks game because I’m happy to be with my daughter on a Sunday night.”

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The middle child in a family full of overachievers, Emanuel seldom if ever second-guesses himself in public. But, the poll — and results that show fewer than one in five Chicagoans credit him with doing a better job running Chicago than Richard M. Daley did — does have him vowing to take a chill pill.

“For all that energy and drive, my wife has recommended to me that, if we ever had a fourth child, she was gonna call it `Patience’ as a way to slow me down. So, periodically, you gotta take [that advice]. No doubt. I should heed her advice,” he said.

“But, when it comes to knowing I could do something and make peoples’ lives different and the only thing standing in the way is the political will to fight for it, I’ll continue to fight on behalf of the children and families of Chicago.”

Emanuel has alienated African-American voters who helped put him in office by instigating Chicago’s first teachers strike in 25 years, closing 50 public schools, opening new charter schools and unveiling plans to build new schools and school additions, with the educational largesse heavily concentrated on the North Side.

That includes a $14 million addition to Walter Payton College Prep and a new, $60 million selective enrollment high school nearby named after President Barack Obama, whose 2011 endorsement of his former White House chief-of-staff sealed the deal with black voters.

The political fallout from those actions and persistent crime showed in the Sun-Times poll.

But at a news conference Wednesday to announce plans to build a Mariano’s grocery store in Bronzeville, Ald. Pat Dowell (3rd) and Will Burns (4th) said there’s still time for Emanuel to restore his standing among black voters.

“A poll is a poll. It’s just a snapshot in time. It could be different tomorrow,” Dowell said.

“Today’s effort to bring a grocery store into the Bronzeville community — something this community has been wanting for a long time — he worked on this. He made it happen. The more that we see those kinds of things, I don’t think a poll is necessarily a reflection of how people really feel.”

Burns called himself a political “hack” and has seen a lot of polls — including one that showed his own state representative down by 13 percentage points six weeks before the election. He ended up winning that 2012 election by five percentage points.

“The messages that have been hitting the African-American community about the . . . mayor’s role on the South and West Sides of Chicago — the voices have been overwhelmingly negative. They have been overwhelmingly critical. And the voices that talk about how the administration has worked cooperatively with aldermen like me and Pat Dowell to bring the kinds of amenities that people in our communities have wanted for years and years and years — that message often gets overshadowed by those who have something negative to say,” Burns said.

“It’s in my vested interest to talk about those things that have happened in the 4th Ward that have benefitted the people of the 4th Ward because we don’t know what might happen under different leadership that may not care the same,” Burns said.

In an interview with the Chicago Sun-Times in March, Emanuel said Preckwinkle had assured him privately that she has no intention of running for mayor.

Emanuel said he took Preckwinkle at her word, even though she’s been the most outspoken critic of the mayor’s school closings, charter openings, school budget cuts and the seven-day teachers strike that Emanuel’s bullying missteps helped to instigate.

Preckwinkle’s camp responded to the mayor’s comments by sending conflicting signals about her political future. About a week later, Preckwinkle pointedly refused to rule out a race for mayor.

On Wednesday, the mayor recounted several instances in which he and Preckwinkle put aside their differences to work together.

Then, he said again, “I trust her when she said multiple times she’s not running. I think she’s a person of her word.”