The toughest Budget package of spending cuts and tax increases in a generation means the UK "can look to a brighter future", George Osborne has said.
The chancellor said "decisive action" to raise VAT and cut spending would boost confidence in the economy.
He also said spending cuts might be reduced if more savings could be found in the welfare budget.
Labour's Alistair Darling said it could be "dire for many" and the coalition might be unable to implement it.
'Confidence in economy'
Mr Osborne put the case for the coalition's "tough but fair" Budget - which will leave households on average £400 a year worse off - in a series of media interviews on Wednesday while David Cameron will face scrutiny by MPs at the weekly prime minister's questions.
In his first Budget, Mr Osborne announced a two-year pay freeze for public sector workers earning over £21,000 and substantial welfare savings including a three-year freeze in child benefit, a cap on housing benefit and a reduction in tax credits for families earning more than £40,000.
He said the main rate of VAT would rise from 17.5% to 20% from next January, a move raising an estimated £13bn and was "unavoidable" given the dire state of the public finances. But he raised the personal income tax allowance by £1,000.
"Because I took decisive action, we're going to have confidence in this economy, the forecasts show unemployment is going to fall, and that is a good news story," Mr Osborne told the BBC.
"I'm not claiming that people are immediately better off as a result of the Budget - I have said that everyone is making a contribution.
"But by increasing the personal income tax allowance for people on the basic rate what I have done is tried to protect low and middle income earners, people who are in work, I wanted to reward work."
He said if he has stuck with Labour's plans "we would now be in a proper economic crisis in this country" and accused Labour of "carping from the sidelines".
In the Budget he revealed that government departments - excluding health and international aid - face an average 25% real terms squeeze in their budgets over the course of the Parliament.
That includes the freeze in public sector pay, which is expected to save £3.3bn a year by 2014-15.
Mr Osborne told BBC Radio 4's Today programme if further welfare savings could be found, it might be lower.
"In the end that's the trade-off that we have got to make in the spending review, not just between departments but also between the very large welfare bill and the departmental expenditure bill."
The government plans to cut the structural budget deficit to zero in the next six years, a goal which the BBC's political editor Nick Robinson said represented a "dramatic change" in political and economic strategy from its Labour predecessor.
In an e-mail to Conservative supporters, Mr Cameron said the cuts and tax rises - representing £40bn of extra "fiscal tightening" on top of that already proposed by Labour - would "bring sanity" to the public finances.
"Will it cost our coalition some popularity? Possibly," Mr Cameron said.
"But is this the right thing to do - for the health of the economy, for the poorest in our society, for the future of our country? I passionately believe it is."
Lib Dem leader Nick Clegg held a meeting with his MPs after the Budget amid signs that dissent in his party is limited at this stage.
Only one Lib Dem MP, Bob Russell, has threatened to vote against the Budget - in opposition to the VAT rise - and senior Lib Dem figures have lined up to back the coalition programme.
Business Secretary Vince Cable said his party had helped secure some "very big and progressive steps" such as raising tax thresholds for the lowest-paid, restoring the earnings link with the state pension and a £150 annual rise in child tax credits for the poorest families.
And the party's deputy leader Simon Hughes said the Budget had gone some way to making the tax system fairer - a key demand in last month's coalition negotiations.
"We have not got all we wanted," he told the BBC News Channel.
"I am not pretending we have. But I am clear that we needed to deal with the huge economic mess we are in and we need to do it a way which is a fair outcome."
But Labour said the Lib Dems had got little in return for their support and their backing for the VAT rise - after they warned of a "Tory VAT bombshell" during the election - meant the public would not trust them again.
Shadow chancellor Alistair Darling told the BBC the previous Labour government had been reducing borrowing "in way that was manageable and deliverable".
"There is a big question mark frankly as to whether this coalition between the Tories and the Liberals will actually deliver on a lot the things they have been promising yesterday.
"This is taking an huge risk. It has been tried in other countries before and it hasn't worked. If you snuff out the recovery too early, you don't get the employment you don't get the revenues coming in, you bump along the bottom and you get high high debt and high borrowing. That would be a disaster for us."
And shadow business secretary Pat McFadden said: "What we are seeing is a lot of familiar Tory songs - VAT increased, child benefit frozen.
"The difference this time is that the Lib Dems are leading the chorus."
Unions say the combination of a public sector pay freeze and a 25% reduction in most departmental budgets will bring real pain and leave many people feeling angry.
"It is savage," said Jonathan Baume, from the First Division Association - which represents public servants.
"There has not been anything on this scale since the 1920s."
* "Britain's economy - Cameron & Clegg Face the Audience" on tonight's Six and Ten O'Clock news or the whole half hour at 7pm on the BBC News Channel or 11.25pm on BBC2.