Conservative MP Fiona Bruce said she had campaigned for the road since taking her seat in 2010.
“I have long been pressing for work on Middlewich Bypass to start.
“No wonder residents are asking, ‘What has Labour been doing all this time?'” she said.
Sam Corcoran, the Labour leader of Cheshire East Council, said the council was “disappointed” at the latest setback, and wanted an urgent meeting with the government.
“This further delay to the approval of the scheme is a further blow to the council’s growth and levelling up ambitions for the borough.
“It will also be a desperate disappointment for the residents of Middlewich, as well as the businesses that were hoping to come to new premises in Middlewich on the back of the bypass being completed.”
In response to Ms Bruce, Mr Corcoran said: “Fiona Bruce claims that she secured nearly £57m of government funding for the scheme in 2017.
“Yet when the government is asked to sign off on £48m, they refuse.
“As with HS2 coming to Crewe, this government flip-flops.”
But while the politicians trade barbs, for many in the town, the announcement that – for now, at least – the bypass is on hold was not unexpected.
“Nothing surprises me,” said one woman outside the town’s library.
“The bypass most probably won’t go up in my time.”