The IHC is appealing a court ruling requiring staff to be paid at least the minimum wage for sleep-over shifts.
But one of the unions representing disability support workers, the Service and Food Workers Union, said it planned to ask the Supreme Court to throw out the appeal as it was a waste of public money and a "hopeless cause".
The Court of Appeal last month upheld an earlier Employment Court decision against an IHC provider, Idea Services, which had opposed paying for sleep-over hours, arguing sleeping was not working.
The appeal court said sleepovers constituted "work" under the Minimum Wage Act because significant responsibility and restrictions were imposed on workers while on sleepovers.
Instead of a shift allowance of about $30, staff would get at least the minimum hourly wage.
But the union said it was the Government, not IHC, that needed to pick up the tab.
"The Government is pressuring IHC to waste public money on more fruitless appeals so that they can delay the inevitable, hopefully till after November's general election," union national secretary John Ryall said.
The Government still refused to acknowledge financial responsibility despite three judicial bodies ruling that the minimum wage needed to be paid, he said.
Overnight staff had been working nights for less than the minimum wage for more than 20 years, he said.
Although IHC provided a service on behalf of the Government, its funding was based on worker pay rates below those specified in the Minimum Wage Act.
The Government was a party to the previous Court of Appeal case but only IHC, the principal appellant, could appeal to the Supreme Court.
The union wanted to start direct discussions with the Government to find a resolution, he said.
IHC spokeswoman Philippa Sellens told NZPA it was seeking leave to appeal because it believed it had grounds.
"We are basically working through every legal avenue available to us," she said.
She agreed it would be helpful if the Government stepped in.
"We have always said that there is no way the Idea Services can pay $176 million in backpay or $30 million going forward and the Government needs to provide a solution."
However, the Government had publicly signalled it wasn't in a position to pay $176m either, she said.
Health Minister Tony Ryall said Idea Services' decision to appeal was understandable considering the significant financial consequences of the previous court rulings.
The Government's position remained unchanged as previous rulings were unaffordable for providers and taxpayers.
The Ministry of Health estimated last year that total backpay for disability support workers could be as much as $500 million.
The Government put IHC subsidiaries Idea Services and Timata Hou into statutory management last October at their request because they were concerned they would not be able to continue to operate.
Labour has said a funding increase was needed to support care providers and that's what it would do in government.