Sinn Féin Cllr Daithí Doolan argued that Mr Skehan had "disqualified himself" from the position
Dublin city councillors have passed a motion calling for the removal of the Housing Agency chairperson from his role.
Conor Skehan was reappointed last Friday, despite having been expected to step down at the end of December.
The Department of Housing has said the reappointment is on a temporary basis while they continue the search for a replacement.
Mr Skehan has, however, faced criticism recently after claiming that some people living in emergency accommodation could be 'gaming the system' to get housing.
The motion calling for Mr Skehan's removal was passed at a Dublin City Council meeting yesterday evening, although was opposed by 20 councillors.
Sinn Féin Cllr Daithí Doolan proposed the motion, arguing that Mr Skehan had "disqualified himself and made himself unable to chair this Housing Agency" because of the comments.
People Before Profit TD Richard Boyd Barrett agrees that Mr Skehan has to go.
Speaking on Newstalk Breakfast, Deputy Boyd Barrett argued: "There's an inaccuracy at the heart of what he's saying.
"I'm dealing with a flood of people in homeless emergency situations... the fact that you become homeless does not put you on the priority list in Dun Laoghaire Rathdown. You have to be considered extremely vulnerable... that may involve homeless, but it doesn't guarantee."