Changing course on the economy would plunge the UK "back into the abyss", David Cameron has said.
The warning followed suggestions by Business Secretary Vince Cable that the government should consider borrowing more to kick-start economic growth.
But, in a speech in West Yorkshire, Mr Cameron echoed Mrs Thatcher by saying "there is no alternative" to "sticking to the plan" on the economy.
Labour said the government's economic strategy had "totally failed".
Mr Cameron said: "There are some people who think we don't have to take all these tough decisions to deal with our debts. They say that our focus on deficit reduction is damaging growth, and what we need to do is to spend more and borrow more.
"It's as if they think there's some magic money tree. Well let me tell you a plain truth: there isn't."
'Into the abyss'
More borrowing would jeopardise the prospect of "good jobs for our children", and the UK's ability to afford "good public services", he argued.
The PM continued: "I know some people think it is somehow stubborn to stick to a plan.
"That somehow this is just about making numbers add up without a proper care for what it means for people affected by the changes we make.
"As far as I'm concerned nothing could be further from the truth. My motives, my beliefs, my passion for sticking to the plan are exactly about doing the right thing to help families and to help businesses up and down the country."
There were now "some signs that we can turn our economy round", he said, citing the reduced deficit, low interest rates, and higher exports to emerging economies like Brazil, Russia, India and China.
"Of course the challenges are huge. And there is, I completely accept, a long way to go," Mr Cameron said, criticising those who "would falter and plunge us back into the abyss".
He concluded: "We are making tough choices about our future. But we are making the right choices. If there was another way, an easier way, I would take it.
"But there is no alternative."
The prime minister said Britain was reaping the rewards of the tough economic course set by the coalition in 2010, and highlighted the creation of one million extra private sector jobs and higher employment rates.
But shadow chancellor Ed Balls said the UK could not afford "two more years of economic failure".
"Families, pensioners and businesses across Britain will wonder what planet David Cameron is on," he said.
"He claims the economy is getting better and his plan is working, but everyone else knows that the economy is flatlining, living standards are falling and the deficit is rising to pay for the costs of economic failure.
"This defensive speech cannot mask the total failure of this government's economic plan and growing divisions in a cabinet which is now openly debating the need for a change of direction."
Writing in the New Statesman, Lib Dem Business Secretary Vince Cable suggested the government might need to change course on the economy and consider borrowing more.
He said the danger of slow growth may now be greater than the loss of market confidence through increased borrowing and that the "balance of risk" had changed since 2010, when the coalition made deficit reduction central.
But asked about his position by the BBC, Mr Cable said there was nothing wrong with the government's current strategy - commonly called Plan A.
"We need to pursue what I've often called 'Plan A Plus' - that's financial discipline and getting down the deficit, and at the same time pursuing growth. That's what we're doing and what we'll continue to do."
The BBC's Political Editor Nick Robinson said Mr Cable's argument was not new but No 10 seemed to have been caught by surprise by the timing of the article, which comes less than two weeks before the Budget and after the economy shrank in the last few months of 2012.
Conservative Mayor of London Boris Johnson told the BBC: "I don't want to intrude on the chancellor's pre budget calculations, but it's definitely my view - and I know it's his view too - that you won't go wrong in this current climate by investing.
"There are plenty of people out there who want to invest in London infrastructure, investing in the big projects, and indeed cumulatively investing in them, to deliver jobs and growth - that is the way forward."
Deputy Prime Minister Nick Clegg, ahead of a meeting with Mr Cable on the government's Budget plans, said there was no division in the coalition over the need to support capital spending which he said was crucial to creating jobs and getting "the wheels of the economy moving".
He told LBC 97.3 that he was frustrated by the slow pace of some current projects but there was a risk that if the government borrowed billions of extra money, this could push up interest rates for ordinary families.
"There is no cost-free, risk-free, magic wand solution to it."