One proposal approved 21-17 by the Republican-led Senate would aim to save money by changing how health insurance benefits for teachers and government workers are managed.
The measure, now headed to the Democrat-led House, is key to the overall budget deal because it could be a trade-off to get Republicans to vote for tax increases.
The House passed bills to create incentives for Medicaid recipients to lead healthy lifestyles, among other reforms, which now are headed to the Senate.
Democratic Gov. Jennifer Granholm has told about 35,000 of the state's more than 53,000 workers not to report to work on Monday if a shutdown occurs. The remaining workers, mostly related to public health and safety, would stay on the job.
A partial state shutdown would mean most government operations would cease, including liquor deliveries, lottery ticket sales, the issuance of driver's licenses and construction on state roads.
Republicans have pushed Granholm to accept a temporary budget that would extend the one currently in place, giving legislators more time to craft a long term deal.
Granholm has said she won't sign a temporary budget unless she has assurances higher taxes to pay for education, public health and other programs are part of the deal.
Leaders in both the Democrat-led House and Republican-controlled Senate are optimistic a deal will be reached to avoid a shutdown.