Mark Butler has doubled down on his plans to pass contentious NDIS changes as early as this month, warning the opposition against using the bill as a “pawn in a bigger game of chess” as they consider a potential deal with the Greens.

The Coalition and the Greens have criticised Labor’s truncated timeline to pass NDIS, negative gearing and capital gains changes, and have signalled they could team up against the government in the Senate to extend inquiries into the bills.

Disability advocacy groups and NDIS providers roundly criticised the proposed NDIS change at public hearings last week while state and territory disability ministers argued they could not replace disability supports for the more than 200,000 participants expected to be shifted off the scheme by 2031.

The health minister said he was “utterly convinced” the federal government’s plan was right, and that it shouldn’t be delayed for further consultation, but didn’t rule out potential amendments.

Butler said a potential six-month extension for the NDIS inquiry could cost the federal budget billions of dollars.

“It would be six months more without the reform that the scheme needs. Six months more of people receiving services that aren’t as good as they should be because a lot of the reforms that we’re putting in place are to improve the quality of supports and services, to improve arrangements around integrity and fighting fraud,” he told ABC’s Insiders on Sunday.

“[Angus Taylor is] simply trying to use this as a pawn in a bigger chess game that he’s seeking to play about other areas of the budget.”

The changes to limit who can access the NDIS – which supports more than 760,000 Australians with disabilities – will reduce participant payments by at least $37.8bn until 2030, according to budget papers.

During a press conference on Sunday announcing his retirement from politics, Liberal frontbencher Jonno Duniam said it was important his party took the time to “get this right” on both the NDIS and tax reform.

“They’re talking about carve-outs on the run and changing bits and pieces of the legislation – taking off as the planes being built has never ended well for our country,” Duniam said.

“To that end, on both pieces of legislation, be it a six-month inquiry for the NDIS or similar, then let’s have a proper look at this stuff and do our job properly in the interests of the people of Australia.”

Phil Thompson, a former shadow assistant NDIS minister, with a child on the scheme, said he wasn’t “too happy” about the government’s proposal.

“All I’ve seen from the government around their language around NDIS and the movements and the cuts there, yet they really make you feel like your loved one is an inconvenient dollar figure on the government’s budget bottom line,” the north Queensland MP told Sky News on Sunday.

The NDIS inquiry is expected to deliver its report on Tuesday while the hearing into changes to capital gains tax discounts and negative hearing will begin on Monday.