Mr Clegg said Warren Bradley, his party's leader on Liverpool City Council, was "wrong" and claimed he was doing the opposition's job for them in calling for a split from the Tories.
In a leaked letter Mr Bradley urged his party leader to act before "we disappear into the annals of history".
He said Lib Dem councillors were set to lose seats in local elections on May 5, and the coalition was to blame.
Mr Bradley went on to write: "We have to sever ties from the coalition; if we fail to do this, we have only our parliamentarians to blame."
But Mr Clegg said his party would not be quitting the Government and had to "stick with the plan".
"I think Warren Bradley is one voice, but I think he is wrong," the Deputy Prime Minister said, during a visit to Rochdale.
"If anyone knows what it's like to clear up the mess after Labour, it is the people of Liverpool.
"We can't do it overnight.
"We are doing something really difficult, we are clearing up this terrible mess we inherited from Labour.
"I think we have got to stick to the plan because that will lead us to hand on a better economy for future generations.
"If we get it right, there is a better, brighter future."
Mr Clegg said in the last week in Liverpool alone, 25,000 pensioners and 140,000 basic rate taxpayers were better off due to reforms brought in by the coalition government.
Mr Clegg responded to Mr Bradley's email to his party leader while he was on a visit to Rochdale to publicise a Government scheme to help finance businesses.
But before touring local engineering firm Holroyd Precision Ltd, the winner of a £2.8 million government grant, he had to face yet another critic.
Gillian Duffy, famously and disastrously branded a "bigoted woman" by Gordon Brown, tackled him about his alleged sell-out to the Tories.
Mrs Duffy, 66, asked he why he "went in" with the Tories instead of Labour after the last General Election.
"Because you may remember, no-one won the election at all. No- one got a majority," Mr Clegg said.
"I think it is important you have a Government that can do things because we have to sort out a lot of mess we inherited from the previous lot."
Unbowed, Mrs Duffy asked the Deputy Prime Minister to "look me in the eye and tell me" he was happy with the current Government cuts.
"Whoever was in power now, any government would have to take difficult decisions," he told her.
Mr Clegg added that the country's finances was similar to him and his wife "maxing" out their credit cards - and the debt had to be paid off.
But Mrs Duffy responded "That's just the same speech" she heard him give an hour earlier on the radio.
Mr Clegg later conceded he had probably not won her vote.
Mrs Duffy said she had failed to be convinced about the coalition Government after the brief exchange with Mr Clegg.
"It's gone wrong," she said, "Let's face it, it's all gone wrong."
Later the Deputy Prime Minister refused to be drawn on Mr Bradley's warning about his party's chances at the looming local elections.
He added: "I think Warren Bradley is making a huge mistake in joining in with all that. Let's leave the criticism to our critics."
The Deputy Prime Minister said rather than "doing the job of our critics for us" like Mr Bradley, his party had to stick to the plan of balancing the country's books, to "deliver a better future".
But the war of words continued despite Mr Clegg's response to the leaked email.
Mr Bradley refused to back down, telling ITV Granada Reports: "This isn't a civil war in the party, this is about me putting across my views.
"Our heartlands are being affected by some of the decisions being made by the coalition.
"I will defend the coalition on some issues. The Labour Party left this country in a hellish mess financially and somebody had to take control of it but unfortunately some of the decisions being taken are against my principles and I know against the principles of a lot of Liberal Democrats in Liverpool."
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