The ruling Labour group is outnumbered by opposition councillors following the recent defection of one member to the Conservatives and two deciding to become independents.
That has added an extra dimension to the contest for the Westfield ward seat where the Liberal Democrats are fielding former council leader Andrew Waller as their candidate.
Council and Labour group leader James Alexander said Mr Waller “oversaw the Barbican fiasco” when in office.
“This election could determine if Labour leads the council or whether the Conservative-Liberal Democrat coalition in Downing Street comes to York’s streets and takes control of the council,” he said.
Lib Dem group leader Keith Aspden said: “Over the last few weeks Labour councillors have given their verdict with three resigning from the group. Now it is the voters chance.
“The residents I have spoken to overwhelmingly feel let down by Labour in York after their cuts to local frontline services in Westfield, the botched closure of Lendal Bridge and the plans to bulldoze over York’s green belt.”
Conservative Group leader Chris Steward admitted it would be a “surprise” if it won in Westfield today.
“However it has been clear from talking to residents that they are sick of Labour and that they support the alternatives we have proposed – whether backing vital local services like salt bins rather than Labour’s choice of an arts barge to keeping council tax frozen.”