The federal health minister has revealed 160,000 people are expected to be shifted off the $50 billion scheme under new eligibility rules.
During an address to the National Press Club on Wednesday, Mark Butler said states would have "greater funding responsibility for the scheme".
Several state leaders said they weren't fully consulted about the changes and didn't want to bear the costs of a federal responsibility.
Western Australia Premier Roger Cook said he supported cost-cutting reform, but didn't want the burden to shift to the states.
"I wish I'd had a briefing, would have been great to see where the NDIS ship is going," the Labor premier said.
"The states have been working with the Commonwealth around reform of the whole NDIS system, taking on more of the foundational supports, ensuring that young people in particular can get the supports they need.
"But it's a Commonwealth program, so we don't want to pay for it."
Queensland Disability Services Minister Amanda Camm said the announcement had come with "little detail and ... little consultation".
"Minister Mark Butler stood up in the National Press Club and outlined the runaway train of which the NDIS has become and, in doing so, simultaneously decoupled the carriages and sent them the state's way," she said.
The Liberal National Party minister accused federal Labor governments of failing to reform the scheme earlier and allowing "shonky individuals" to take advantage.
"It was the federal government that determined disability would be their responsibility," she said.
"It will be our state and other states and territories that will pay for the failures.
"Mr Butler outlined that local support systems need to be rebuilt by states and territories. These systems don't exist and they will come at a great cost to our state to rebuild."
Tasmanian Premier Jeremy Rockliff said he was yet to be briefed fully on the NDIS changes, but the scheme's integrity relied on support going to those who needed it most.
"The NDIS was set up with very good intent and very good purpose - that purpose must be maintained," the Liberal premier said.
A spokesperson for the NSW government said ministers would be briefed on Wednesday evening and they would "carefully review the announcements and the impact they have" on the state.
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