SACRAMENTO — California lawmakers approved a $400 billion-a-year program Thursday that would completely overhaul how Californians receive their health coverage by creating a single government-run, universal-care system for everyone in the state.

The state Senate approved the bill to create the Healthy California system 23-14, despite many lawmakers acknowledging that significant details remain unanswered, including how the state would pay for and provide care for its 39 million-plus residents. A legislative analysis of the bill warned that the $400 billion-a-year cost estimates “are subject to enormous uncertainty.”

SB562, by Sen. Ricardo Lara, D-Bell Gardens (Los Angeles County), now heads to the Assembly, where it’s expected to face tough opposition. A legislative analysis said that about $200 billion could be raised from a new 15 percent payroll tax, which would require a two-thirds vote from both houses. The other $200 billion could come from existing federal, state and local spending on health care. But the federal government would have to approve any changes to Medicaid funds for the program.

The total cost would surpass the state’s annual budget of $180 billion. Lara said ahead of the vote Thursday that the bill is a work in progress. However, he urged lawmakers to pass the bill to allow him to continue to work on it.

“We know those who do not have access to care have significantly worse health outcomes and are disproportionally people of color and working poor,” Lara said. “It’s time to say once and for all that health care is not a privilege for those who can afford it.”

The bill calls for rebuilding health care in California from a multi-payer system to a single payer “fee-for-service” system, taking the state into unknown territory with unanswered questions about how “enrollees, providers, employers, and the state would adapt,” according to a legislative analysis. The new program would upend the health insurance industry in the state, leaving thousands unemployed, and the state would set aside funds to retrain that workforce.

It would also eliminate premiums, co-payments and deductibles and allow Californians to get health care from any willing provider without referrals.

Anthony Wright, executive director of the consumer advocacy group Health Access, said the bill has a long way to go, but that SB562 “puts forward a compelling vision of what our health system could be, one that is more universal, efficient, simpler, and focused on patients and prevention rather than profits.”

Critics of the bill said the cost would be too much for the state to bear.

“How do we possibly pay for this thing?” asked Sen. Tom Berryhill, R-Modesto, ahead of Thursday’s vote. “This seems to me to be like what we did originally with Covered California and we are going to just figure it out as we go. ... We don’t have the money to pay for this.”

Charles Bacchi, president of the California Association of Health Plans, said the bill would cause “dangerous disruptions in health coverage and quality of care” for millions of Californians.

The Senate’s approval of the bill comes ahead of the “house of origin” deadline on Friday, by which time bills have to be approved in the house where they have been proposed so that legislation can be swapped between the Assembly and Senate.

After Friday’s deadline, the Legislature will have until Sept. 15 to send finalized bills to Gov. Jerry Brown.

Among other bills that have already made their way through their first house is SB54, by Senate President Pro Tem Kevin León, D-Los Angeles, which would force all city and county law enforcement departments to follow the type of sanctuary policies that many of the larger cities, including San Francisco and Oakland, embrace.

SB54 passed the Senate in April and is currently in the Assembly.

Some other bills that passed their houses this week include:

• SB10, by Sen. Bob Hertzberg, D-Van Nuys (Los Angeles County), would eliminate jail time for people accused of non-violent offenses who are awaiting trial. The bill seeks to address a bail system that critics argue penalizes the poor, who often are incarcerated while awaiting trial because they cannot afford bail. SB10 passed the Senate and heads to the Assembly.

• SB149, by Sen. Mike McGuire, D-Healdsburg, and Sen. Scott Wiener, D-San Francisco, would require presidential candidates to release the last five years of their tax returns in order to appear on the California ballot. The bill is a response to President Trump refusing to release his tax returns. The bill passed the Senate and heads to the Assembly.

• SB239, by Wiener and Assemblyman Todd Gloria, D-San Diego, would reduce from a felony to a misdemeanor the crime of willfully transmitting HIV. The bill passed the Senate and moves to the Assembly for consideration.

• SB179 , by Sen. Toni Atkins, D-San Diego, would create a third gender option on driver’s licenses and birth certificates for “nonbinary” people who do not identify as either male or female. The bill passed the Senate and heads to the Assembly.

• SB30 , by Lara, would ban the state from working with companies on the construction of Trump’s proposed border wall. Lara said Thursday that he believes the wall will never be financed and thus will never be built, making the bill more about standing up to the Trump administration and its policies. The bill passed the Senate and heads to the Assembly.

• AB932 , by Assemblyman Phil Ting, D-San Francisco, seeks to reduce regulatory delays on housing for the homeless by allowing San Francisco and San Diego to create their own own local standards instead of following state and local building, housing, health and safety laws during a shelter crisis. Other cities could sign on as well. The bill unanimously passed the Assembly and heads to the Senate.

• SB384 , by Wiener, would allow cities to extend alcohol sales to 4 a.m. The nightlife bill passed the Senate and now heads to the Assembly.

• AB73, by Assemblyman David Chiu, D-San Francisco, would give local governments money to increase housing near public transportation. The amount set aside would be subject to budget negotiations. The bill passed the Assembly and heads to the Senate.

• AB1120, by Assemblyman Jim Cooper, D-Elk Grove (Sacramento County), would require retailers who sell butane to keep certain information about the purchaser. Butane is a colorless and odorless liquid that can be used to make hash oil. The flammable material has caused explosions in homes and apartments where the THC-laden hash has been made. The bill passed the Assembly and heads to the Senate.

Melody Gutierrez is a San Francisco Chronicle staff writer. Email: mgutierrez@sfchronicle.com. Twitter: @MelodyGutierrez