New hires would pay 30 percent toward their premiums immediately.
In addition, the plan calls for increasing co-pays and giving workers more health plans from which to choose, but details have not yet been laid out.
"Ultimately, we project annual savings at $871 million once the 30 percent premium share is fully implemented in 2014," state Treasury Department spokesman William Quinn said.
The governor's proposal is largely modeled after the federal health-care plan and would mean a significant increase in contributions by state workers, who currently pay 1.5 percent of their salary. On average, the state workforce pays about 8 percent of the cost of premiums.
Democrats have questioned the amount of savings projected, saying the administration has yet to propose legislation because doing so would prompt an independent evaluation from the nonpartisan Office of Legislative Services.
Quinn declined to provide a breakdown of savings. But in the budget proposal, the administration says that if the governor's plan is adopted, the state would save $323 million in the 2012 budget year, which begins in July.
"I can't make heads or tails of where they come up with the numbers," said State Sen. Paul Sarlo, chairman of the Senate Budget Committee. "I'm willing to listen and learn about it, but that's a lot of savings.
"We keep asking questions and they keep telling us they will get back to us with the answers," said Sarlo (D., Bergen).
State Senate President Stephen Sweeney (D., Gloucester) has also offered a phase-in plan, one that more closely ties salaries to the level of contribution. His plan has a sliding scale of 12 percent to 30 percent of the cost of the premium, based on income and phased in over seven years.
Within seven years, top-tier workers making more than $100,000 would also contribute 30 percent of the cost of their premiums while those making $30,000 or less would pay 12 percent of their premium.
The Office of Legislative Services has estimated that Sweeney's plan would save $206 million when implemented.
Sweeney's proposal also calls for increasing the number of health-care plans offered to state workers.
A spokesman for Sweeney declined to comment on the governor's proposal.
The state's largest workers union, which is pushing to reform benefits through collective bargaining rather than legislation, has also put forward a plan. It would have workers continue to pay 1.5 percent of their salary and 8.5 percent of their premium by the fourth and final year of a new contract.
Communications Workers of America officials said that their plan would save the state $240 million but that the governor has refused to acknowledge it.
"This belongs not in the newspapers, but at the collective-bargaining table," CWA state director Hetty Rosenstein said of the governor's proposed overhaul. "We presented the governor with a health-care proposal on March 11 and received no response."
Christie, who has made a national name for his fights with union leaders, especially teachers, has said he won't bargain over pension and health-care reform.
Sweeney says he is open to reform through either the negotiating table or legislation.