CHICAGO (CBS) – Ald. Sandi Jackson (7th) was back at City Hall on Tuesday, making her first public appearance since her husband, Jesse Jackson Jr., resigned from Congress last month. The alderman shot down rumors she’s planning to resign, and also insisted she’s not planning to run for her husband’s empty seat on Capitol Hill.

CBS 2 Chief Correspondent Jay Levine reports Alderman Jackson has had a tough time in recent weeks – with her husband resigning amid allegations of possible misuse of campaign funds and undergoing treatment for bipolar disorder.

With her husband’s defense lawyers negotiating a plea deal with federal prosecutors, there might have been times when she said to friends that maybe she should just quit and do something else.

She said it to Levine in private just a few weeks ago, but that’s not the way she feels today. She denied news reports that she had confided to friends she planned to step down as alderman.

“I’m not resigning. I am here, I am working, I’m going to continue to work, and whoever these people are who purport to speak for me should stop! I’m asking them please to stop,” Jackson said.

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Jackson said she intends to stay on as alderman.

“I am back to work today, I was at work last week when we had the shooting,” she said. “I’ve been meeting regularly with our [police] commanders to try to figure out we can stem a lot of this gang activity that’s going on.

Just before her first appearance in the City Council Chambers in more than a month – greeted by colleagues and coworkers – she tried to explain why some thought she could have thought she might resign.

“It would be hard for any family to go through what we’ve gone through publicly, and so there may have been times when I was overcome with exhaustion, I was overwhelmed, and felt as if I couldn’t take another step. That’s real, and that’s human,” she said.

But now, she said, things are improving. She’s back at work in Chicago. Her husband, the former congressman, though still facing criminal prosecution, was staying at their home in Washington, D.C., where their two children attend school.

“I feel incredibly encouraged, happy to have Jesse back at home,” he said. “He’s doing so much better and we are seeing him improve every day.”

Also contrary to some speculation, Alderman Jackson said she’ll be on the sidelines as a large field of candidates fights for the right to replace her husband in Congress.

“I am not a candidate for Congress,” she said. “I intend to remain an alderman. I intend to continue to work by the mayor’s side.”

Mayor Rahm Emanuel has been sympathetic toward Jackson and her struggle.

As the official campaign manager for her husband, it stands to reason that her actions are also being scrutinized by federal investigators combing through the campaign spending records.

However, she said the only complaint she’s heard so far was from her husband, for spending too much money on muffins for volunteers.