TALLAHASSEE -- A new Senate proposal would force many state employees to pay thousands a dollars a year more for health insurance --- or choose skimpier coverage.

The bill, filed this week to help carry out the Senate’s budget plan, would provide $500 a month to help cover each worker’s health costs, whether the worker is single or has a spouse and children.

For rank-and-file employees with family coverage, that would be about $500 a month less than the state provides this year.

The proposal, coupled with other changes in the bill, would save the cash-strapped state $351 million during the fiscal year that starts July 1, according to a Senate staff analysis. Gov. Rick Scott made a similar proposal in January — though the House has not gone along with the idea in its budget plan.

Sen. Bill Montford, D-Tallahassee, said the proposal would be "devastating" for many state employees. He said they have not received raises in four to five years and also are facing legislative proposals that would force them to start contributing money to the state pension fund.

"There’s a question of, how much can they take?’’ said Montford, whose district is filled with state workers.

Senate President Mike Haridopolos’ office did not respond to questions about the bill late Wednesday afternoon. But Haridopolos in the past has expressed support for making state-employee benefits more like private-sector benefits.

Some Republican leaders have pushed for increased use of what are known as "health-savings accounts.’’ Those accounts build up money to pay out-of-pocket medical costs and are coupled with high-deductible insurance plans to pay catastrophic expenses.

Reducing the state’s contribution for health insurance could spur more workers to use health-savings accounts and high-deductible plans. That is because such plans have lower premiums — but also provide less coverage than traditional insurance plans.

The bill makes clear the state would spend a maximum of $6,000 a year — or $500 a month — on each worker and puts the onus on employees to cover the rest.

"Remaining premium requirements shall be the responsibility of the enrollee, based upon plan selection,’’ the bill says.

The Senate Budget Committee likely will take up the proposal Thursday, along with dozens of other budget-related bills. Ultimately, the Senate and House would have to reach agreement on such a proposal before it could take effect.

Along with reducing the state’s contribution for employee coverage, the Senate bill also would make several other changes in the insurance program. As an example, it would add a new actuarial requirement that likely would lead to higher premiums for retirees who buy coverage through the state insurance plan.

Also, the bill calls for the state to self-insure the plan, which offers a choice of coverage through preferred-provider organizations and health-maintenance organizations. The state already self-insures the PPO part of the plan but does not self-insure the HMO portion — and a recent study said such a change would save money.

Many of the changes in the bill would take effect in January. Single workers would appear likely to notice little change if lawmakers reduce the money provided for health insurance.

That is because the state already pays $500 a month toward single coverage, with workers picking up $50 as their share. Employees with family coverage pay $180 a month this year.

Doug Martin, a lobbyist for the American Federation of State, County and Municipal Employees, said the proposal likely would lead some employees to leave state government for private-sector jobs. He said health and pension benefits are a major reason that workers stay in state jobs.

"This (bill) is very, very short-term thinking,’’ Martin said.