California may be losing its chance to set the U.S. agenda for providing health care to millions of uninsured because a bill backed by Gov. Arnold Schwarzenegger aiming to do just that is on its deathbed, state lawmakers said on Friday.

California's Republican governor has made medical insurance legislation a top priority and the bill before the state Senate, which votes on Monday, is a compromise crafted with Assembly Speaker Fabian Nunez, the top lawmaker of the Democrat-led chamber.

But some senators say they have heard enough to vote no on the legislation, which would require all Californians to have health insurance, either through private providers or a subsidized state pool funded by taxes on cigarettes, hospitals and employers.

Millions lack medical insurance in the United States and California's efforts to provide it are being closely watched because it has has the largest state population and major political clout. In addition, the issue is front and center in a presidential election year when voters are anxious about rising health-care costs.

While the state Assembly was eager to advance the bill, the Democrat-led Senate is very much undecided.

"Once fully implemented, over 70 percent of California's 5.1 million uninsured, most of whom are low-income working individuals and their families, including 800,000 children, will no longer be uninsured for health care," according to a statement on the bill from Nunez's office.

Republicans in the Senate's minority fear the bill will require near- and long-term tax increases, while Democrats in the Senate are concerned the bill is too vague to make good on its goals and could cost far more than initial estimates.

Schwarzenegger's administration is hopeful those concerns can be overcome by Monday's vote.

"We're continuing to talk, continuing to work," said Sabrina Lockhart, a spokeswoman for the governor. "This is a comprehensive plan that reflects hundreds of hours of work, if not thousands of hours, lots of compromise and feedback."

If the Senate approves the plan and Schwarzenegger signs it, voters would be asked to vote on it.

With a state budget deficit expected for the remainder of California's current fiscal year and the next year starting in July, California cannot afford an ambitious medical insurance experiment, said Republican state Sen. Tom McClintock.