Public Service Association says its members should not have to go through an extended legal fight with the Government just to get paid the minimum wage.
The Court of Appeal ruled in February that caregivers are entitled to the minimum wage rate for every hour spent on overnight sleepover shifts, instead of an allowance that is much less.
The Supreme Court is to hear a Crown appeal in September.
The PSA says it's confident the Supreme Court will also rule in their favour.
National Secretary Richard Wagstaff told Morning Report that union members have overwhelmingly rejected a Government offer of $45 million to cover arrears and minimum wage rates in four years.
Mr Wagstaff says that falls well short of what members of the PSA and the Service & Food Workers Union are owed.
He said he wants to see an end to the court processes and a return to negotiations.
Health Minister Tony Ryall says the liability rests with employers, but the Government has stepped in to protect services for disabled people.
He told Morning Report what the unions want is beyond what the employers, or the Government, can afford.