Kanata Coun. Marianne Wilkinson and fellow city councillors Maria McRae and Jan Harder want the mayor to hand over some of his responsibilities to councillors.
A local newspaper quotes Harder as saying O'Brien's administration is similar to a "train wreck."
Harder seemed to back away from that statement during a radio interview, Tuesday morning.
She says her riding has launched a "Triple B" movement to "Bring Back Bob" - a reference to former mayor Bob Chiarelli.
Meanwhile, Wilkinson told CTV News she doesn't think the mayor is an embarrassment but she does think he needs help dealing with city business.
"That's not exactly what was said," Wilkinson said, referring to a report she said Mayor O'Brien was "embarrassing the city."
"What I was talking about was how we could get together as a group of three to help the mayor in some of the difficulties that he's been facing," she said.
"I don't think he's an embarrassment. I think he's having awkward times," Wilkinson told CTV News.
"I think he needs to do more consultation before he comes out with his suggestions because I think that would smooth things over a lot more," she said. "We have to work as a team - we can't just work as individuals."
Last week the mayor told reporters about his plan to propose a snow surcharge to deal with a shortfall in the budget for this year's snow removal.
O'Brien didn't consult council before alerting the media to his idea.
Wilkinson says the three councillors are simply offering the mayor help to efficiently deal with city business.
Wilkinson told CTV News she believes the mayor's criminal charges are lending to the embarrassment other people tell her about when they watch how the City is run.
"I think that's part of it," she said, also noting O'Brien's lack of experience as another factor.
"The charges have not made it any easier for him or for the rest of council," she said.
O'Brien has faced criticism for continuing his term as mayor despite charges that he attempted to influence Ottawa's 2006 mayoral race.
Police spent eight months investigating claims by Terry Kilrea that O'Brien offered him a position on the National Parole Board to leave the race for mayor.
The investigation was sparked by a complaint from the Ottawa and District Labour Council.
Kilrea alleges he was offered $30,000 to cover his expenses; Kilrea eventually dropped out of the mayor's race, but said he never accepted any money.
O'Brien denies the bribery allegations, along with the claim he discussed a possible appointment for Kilrea with federal Environment Minister John Baird, a Conservative Ottawa MP and the Treasury Board president during the period in question.
The case is scheduled to go to trial April 6, 2009.
O'Brien was also in the news last week when one of his top officials called a radio talk show to endorse his controversial snow surcharge proposal.
David Gibbons was one of few callers to call a CFRA talk show to support the mayor's proposed snow tax. Gibbons hid his true identity and said he was a resident named 'Tom.'
Gibbons resigned later that day.