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Prime Minister Tony Abbott insists he will not be deterred by disastrous polling results following his government's first budget, saying the public had been "on notice" that the Coalition would have to make tough decisions.
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Mr Abbott also said his government had not broken a pre-election promise not to make any cuts to health or education.
The latest Fairfax-Nielsen poll, released on Monday, shows Labor leading the Coalition in two-party preferred terms by 56 to 44 per cent.
Mr Abbott's personal approval rating dropped by 21 percentage points following the budget, which 53 per cent of respondents believe is bad for the country.
"I don't think anyone really expected that you would get a soft-option budget and obviously it's not a soft option budget from the Coalition," Mr Abbott told ABC radio.
"But it's the budget Australia needs at this time if we are going to get Labor's debt and deficit disaster under control.
"I think the last government which brought down a very tough budget – the Howard government in 1996 - took a big hit in the polls too.
"But in the end we weren't elected to take easy decisions but to take hard but necessary decisions and that's what we've done.
"In the end my job is not necessarily to win a popularity contest; my job is to run the country effectively."
Nielsen polling following the 1996 budget showed that 47 per cent of voters were satisfied with the budget compared with 29 per cent dissatisfied.
Mr Abbott said the government's most important pre-election promise was getting the budget back on track towards a surplus.
"I think the public were on notice that we were going to have to make some very tough decisions," he said.
"We've made them. We're not making them for our own political benefit obviously. We're making them for the long-term economic benefit of the country and that's what I believe people elected us to do."
Although state and territory governments are furious about an $80 billion reduction in funding for schools and hospitals in the budget, Mr Abbott said: "There are no cuts to health or education.
"We never said we would honour the Rudd and Gillard government's pie-in-the sky promises in the out years."
NSW Premier Mike Baird said his state would lose 300 public hospital beds if the federal budget cuts went ahead.
"These funds go directly into frontline services, directly into the provision of hospital beds; across the country it's the equivalent of 1200 hospital beds, 300 beds here in NSW," he told ABC radio.
"We are determined to provide the critical health services we need here in NSW. But what we have seen handed to us from Canberra is a long-term trajectory that really puts that at threat - and that's not acceptable for anyone in NSW.
"It's not acceptable for Canberra to just allocate and cross-shift that towards the states without any form of engagement or consultation."
Victorian Liberal Premier Denis Napthine said the cuts would have an immediate impact. "We need to sit down and sort that out," he said.
South Australian Labor Premier Jay Weatherill said states and territories would cause the "maximum amount of political pain possible" if the government proceeds with the cuts.