The lower house's schedule has been cleared on Tuesday and Wednesday for the National Anti-Corruption Commission legislation to be debated and passed.
The Labor caucus meeting on Tuesday approved government amendments to the legislation.
Independent senators Jacqui Lambie and David Pocock have indicated they will support the government's legislation to deliver the commission when it hits the Senate.
Under the government's model, public hearings would only be held in "exceptional circumstances".
Senator Pocock said the high bar remained an issue, but a commission was long overdue.
Senator Lambie said the exceptional circumstances test smacked of a deal done between the government and coalition to ensure bipartisanship.
"We want police on the beat and we want it to get started now," she told the ABC on Tuesday.
Attorney-General Mark Dreyfus on Monday called for cross-party support for the bill.
"This government stands ready to deliver, and I call on all sides of the parliament to join us in that task," Mr Dreyfus said.
Deputy Liberal leader Sussan Ley told reporters in Albury on Sunday that "agreements" had been made to deliver the commission.
The anti-corruption body is set to cost $262 million over the next four years. It would operate independently of the government, and have powers to investigate serious or systemic corrupt conduct across the Commonwealth public sector.
But Mr Dreyfus has previously defended his government's proposed body, saying national security concerns and court proceedings were among the reasons public hearings should not be the default.
The Albanese government pledged at the May election to legislate an integrity commission before the end of the year.
