Speaking at a Senate committee hearing, Engler blamed the Justice Department for failing to help stop judges' "micro management of state prisons" through consent decrees more than a decade old.
However, Associate Attorney General John Schmidt testified that the Justice Department supported the new law and was merely trying to protect the legislation from constitutional challenge.
Engler called the situation "frustrating" and "disappointing."
He said it has cost the state some $200 million to comply with the judicial decrees for prisons.
"We had hoped this law would allow for the rapid wrapping up of some of the consent decrees," he told the Judiciary Committee senators - including Sen. Spencer Abraham (R-Mich.), who had pushed for the new law.
"I do not see an end in sight," Engler said.
Abraham also expressed frustration, saying the law was designed to end "seizure by judges of the power to run prison systems."
In Michigan, judicial orders have federal courts monitoring state prisons to determine how bright the lights are, whether there are electrical outlets in each cell and whether the prisoners' hair is cut by licensed barbers, Abraham said.
Abraham said he was concerned the Justice Department was allowing judges to drag out their oversight of prisons by arguing that judges need not decide the status of the decree within 30 days or temporarily revoke the decree, as the law states.
Also, Abraham was concerned judges might assume indefinite oversight of a prison while they investigated whether any constitutional violation of prisoners' rights took place.
However, Schmidt said the 30-day deadline for a ruling on whether a state had complied with the court decree likely would be a violation of the separation of powers between the congressional and judicial branches.
Schmidt said the Justice Department has argued the court should be allowed only the time necessary to determine if prisoners' constitutional rights were violated on specific items covered by a decree.
Sen. Ted Kennedy, D-Mass., called the bill an unwarranted intrusion by Congress on the judicial branch and said Republicans "have only themselves to blame.
"They passed a bad bill, and they are now asking the Justice Department to defend the indefensible," he wrote.
In Michigan, Engler wants three prisons free from judicial decrees - the State Prison of Southern Michigan in Jackson, the Michigan Reformatory in Ionia, and the Marquette Branch Prison.
Schmidt said consent decrees covered the prisons starting in the mid-1980s because of "flagrant and egregious conditions" at the facilities. The decrees covered medical and mental health care, fire safety, sanitation safety and hygiene, crowding and protection from harm and access to courts and legal mail, he said.
Officials at the Justice Department and the state of Michigan jointly toured the Ionia and Marquette prisons and this year asked that most of the judicial requirements be dropped.
In July, the motion was granted, although it did not cover medical and health care and several other complaints.
The Justice Department has similarly started a series of tours of the Jackson prison. Schmidt said the law requires the courts to examine evidence from the tours promptly.
"It seems to me the process in Michigan is moving forward to resolve the issues," Schmidt said.