Prime Minister Tony Abbott says he is open to "horse trading" to get his government's first budget and associated laws passed by the Senate.
Labor and the Greens will allow the budget appropriation bills - which channel money to departments and agencies - through parliament.
But a number of controversial measures from Tuesday's budget will require changes to other legislation, which could be blocked by a combination of Labor, the Australian Greens and crossbench senators.
Draft laws to impose a deficit levy on Australians earning more than $180,000 were introduced to the lower house after the budget speech on Tuesday night.
The reintroduction of six-monthly petrol tax rises will be the subject of separate yet-to-be-introduced legislation, as will age pension indexation and eligibility changes and the $7 Medicare co-payment.
An $80 billion cut to school and hospital funding over a decade won't require legislation as the funding is in intergovernmental agreements.
Labor says it will oppose the pension age rise to 70, the $7 Medicare co-payment and the fuel tax rises.
Crossbench senators, including the three Palmer United Party senators, have voiced concerns about the same measures.
Mr Abbott said Labor owed it to voters to support the budget because the previous government was responsible for the mess.
"It's like the people who started the fire complaining about the fire brigade knocking down a fence to get to the property," he said.
Mr Abbott said the coalition was happy to talk "respectfully" with the independents and minor parties.
"Obviously a certain amount of horse trading is something that you just accept is part of the business," he said.
What the prime minister won't accept is an attempt to completely frustrate the business of government.
If it came to a double-dissolution election, "hardly any" of the crossbench senators would be re-elected, which made it all the more likely the government would get co-operation.
Palmer United Party leader Clive Palmer, who will have three senators after July 1, has criticised the deficit levy, pension changes and Medicare co-payment.
Labor Senate leader Penny Wong said the opposition would talk to crossbench senators about the legislation.
"People across the political spectrum are united on this issue - this is a vicious budget," she said.
Facing a Labor call to apologise to voters for breaking his election promises, Mr Abbott told parliament the Australian people would get a chance in 2016 to test whether the government had fulfilled its pre-election promises.
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