Prime Minister Tony Abbott is unfazed by bad polls for the government, saying voters will understand the coalition's "elemental commitment" to fix the budget.
Newspoll and Fairfax-Nielsen opinion polls show a sharp drop in the primary vote for the coalition after last week's federal budget, putting Labor in an election-winning lead.
Labor leader Bill Shorten has also taken an 11-point lead over Mr Abbott as preferred prime minister.
Anger over budget measures boiled over on the weekend, with street marches through major cities and a meeting of premiers in Sydney on Sunday vowing to fight $80 billion in school and hospital funding cuts.
Mr Abbott, who visited a medical research facility in Brisbane on Monday, said selling a tough budget was never going to be easy.
"This has been a tough budget, but it has also been a visionary budget," he said of plans for a $20 billion research fund, paid for by a $7 charge for visiting a GP.
Mr Abbott said the Howard coalition government had also taken a hit in the polls after the 1996 budget, which also included large cuts to public spending.
However, the Nielsen poll figures from that period showed 47 per cent satisfaction with the budget, compared with 33 per cent now, and 29 per cent dissatisfaction compared with 65 per cent now.
Facing claims of breaking election promises, the prime minister said the coalition's four "elemental commitments" were to stop the boats, scrap the carbon tax, build roads and get the budget under control.
"We are delivering on all four of them," he said.
Premiers and chief ministers want an emergency meeting with the prime minister before the end of July, saying cuts to health and education funding will have an immediate impact on services.
Mr Abbott said hospital funding was still set to rise, but not as much as under Labor's "pie in the sky" plan.
Victorian Liberal premier Denis Napthine said the cuts would have an immediate impact.
"We need to sit down and sort that out," he said.
The prime minister also faces hurdles to convince Senate cross benchers to pass legislation to bring in the Medicare co-payment, reintroduce indexed tax rises on petrol, raise the top income tax rate temporarily, deregulate university fees and tighten pension and welfare eligibility.
Mr Abbott again said he would be talking to cross benchers "with courtesy and respect" in coming weeks.
Opposition Leader Bill Shorten said he understood the anger among the premiers and protesters over the weekend.
Mr Abbott had been "put on notice" to make the budget fairer and the Senate was the place to make it happen.
The Senate's original purpose was to "protect the states against the capricious and unreasonable activity" of a party with a lower house majority.
"This budget is most certainly an unreasonable and unfair attack on pensioners, on the sick, on the needy and on the poor of our society," Mr Shorten told reporters in Melbourne on Monday.
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