Nick Clegg, the deputy prime minister, has rejected a call from a senior Liberal Democrat councillor to pull out of the coalition government.

Warren Bradley, the leader of the Liberal Democrats in Liverpool, said he was "tired of defending the indefensible" and urged Clegg to act "before we disappear into the annals of history".

In a private email to Clegg, leaked to the Liverpool Echo, Bradley said long-serving Lib Dem councillors in Liverpool were going to lose their seats in the 5 May elections "not because of their record, but because of your record and the perception of what we as Liberal Democrats now are".

Bradley, who was council leader until last year's election, warned the party leader: "Unfortunately the boil is about to come to a head and burst (probably on election night) when we lose some very well respected and experienced colleagues from Liverpool city council."

Bradley said the Lib Dems needed to "reconsider what and who we are before we disappear into the annals of history as a political party who promised so much hope, yet failed because they wanted control and power".

The party had "deserted their followers", he said.

He told Clegg: "I hope you take this in the spirit it is meant, liberal principles have to shine through, we have to be independent and we have to sever ties from the coalition; if we fail to do this, we have only our parliamentarians to blame."

But Clegg said Bradley was wrong. The Lib Dem leader told ITV's Daybreak: "These are very difficult times, and I'm not denying we're having to make controversial decisions, as anybody would who had come into power after the election last May, because we're cleaning up a terrible mess that was left behind.

"I think actually, Warren Bradley and everyone in Liverpool knows what it's like to clean up the mess left by Labour, that's exactly what Liberal Democrats in Liverpool had to do."

A Lib Dem spokesman said Bradley's email "simply does not reflect the views of the wider Liberal Democrat membership".

He said: "Moving from a party of protest to a party of power has brought with it some very difficult decisions but we cannot hide from the fact the country is borrowing an extra £400m every single day – the cost of a new primary school every 20 minutes."

He added: "Liberal Democrats are proud to be fighting, as always, on our strong record in local government and now for the first time in 65 years, on delivering in national government.

"Despite these very difficult times, the Liberal Democrats are delivering on proposals to help people in Liverpool and across the whole of the north-west."

Speaking on BBC Breakfast, Vince Cable, the business secretary, said digging the country out of the "enormous economic hole" would take time but the government would succeed, including in cities such as Liverpool.

"That's a long-term project, it's going to take the five years of this parliament," he said.

"We've got to show stamina, this is a marathon not a sprint and I would recommend to Warren Bradley, who is an admirable Liberal Democrat, that he concentrates on the excellent record of the Liberal Democrats of restoring Liverpool after the terrible mess it was in.

"They should really concentrate on that and the mistakes made by the Labour council and not give up because this is a long-term project but we will turn the British economy around, and the Liberal Democrats in Liverpool and everywhere else will benefit from that."