"It is astounding that Walker is putting the demands of ideological extremists over the interests of health care consumers across Wisconsin who need access to quality affordable health care options," said Robert Kraig, director of the liberal advocacy group Citizen Action.
U.S. Sen.-elect Tammy Baldwin, a Democrat and supporter of the health care law, said Walker "chose to pass the buck and reject the opportunity to take ownership of this issue."
Incoming Republican state Assembly Speaker Robin Vos said Walker was protecting taxpayers from what he said "could ultimately become a major financial catastrophe."
State Sen. Alberta Darling, R-River Hills, co-chair of the Legislature's budget committee, said, "It would be irresponsible to commit our state to a program that isn't fully defined yet," she said.
Opposition to the law remains strong among Republicans. Nine Wisconsin GOP lawmakers went so far as to tell the tea party group Campaign for Liberty that they would back legislation to arrest federal officials who took steps to implement the Affordable Care Act.
Walker stopped implementation last year on the hopes the law would be overturned either by the U.S. Supreme Court or Republicans following the November election. But the Supreme Court upheld the law in June and Obama's victory earlier this month ensured the law's survival.
Walker said despite his opposition to the law, his decision to have the federal government run the exchange in no way means he will stand in the way of it being implemented.
"We're not going to refight the Obamacare debate," he said. "We are going to comply with the law."
As of Friday, 23 states plus the District of Columbia said they would run their own exchanges or partner with the federal government while 15 states, including Wisconsin, said they would defer to the federal government. Twelve states had yet to decide.
Walker announced the state's intent even though the Obama administration late Thursday agreed to a request by Republican governors for a month's extension for making a decision.
The law is expected to provide coverage to more than 30 million people nationwide through the exchanges and expanded Medicaid programs. The Medicaid expansion is voluntary and Walker said Friday no decision had been made on whether Wisconsin will do it.