Conservative councillors said the move could help struggling businesses in January and February.
And city centre businessman Phil Pinder called on councillors to support the plans, saying it could help tackle what are expected to be "dire" trading conditions at the start of the year.
But Andrew McGuinness speaking for York Quality Bus Partnership said the move would encourage people back into their cars, increasing traffic and worsening air quality.
And a spokesperson for York Cycle Campaign raised concerns about safety if the plan encouraged more cars onto the roads.
They also called for the council to relax the rules around people cycling on pedestrianised streets.