UPDATE, October 12, 2:26 p.m.: Gov. Jerry Brown (D) on Thursday signed the bill guaranteeing roughly 2.7 million California parents who work for small companies the opportunity to bond with birth, foster, and adoptive children without fear of losing their jobs.

When Alfonso Garcia’s daughter was born, his employer, a small San Jose, California, area tow truck company, turned down his request for two weeks off, even though Garcia qualified for paid parental leave.

Garcia worked for a small company, one with fewer than 50 employees. If Garcia took time off, there was no guarantee under existing law he’d have a job when he returned.

“I felt stressed out,” Garcia, 27, told Rewire. “I was worried I’d lose my job, and then I wouldn’t be able to care for my family,” said Garcia, the breadwinner for his wife and newborn daughter.

Although the the state’s family leave program provides up to six weeks of paid time off to care for a new child, polling suggests nearly two in five employees don’t use it for fear of losing their jobs.

A new bill in the state’s Democratic-held legislature would change that, guaranteeing roughly 2.7 million California parents who work for small companies the opportunity to bond with birth, foster, and adoptive children. SB 63 extends job protections to small employers, requiring businesses with between 20 and 50 workers to allow workers to take up to 12 weeks of leave to spend with a new child—without fear of losing a job. Right now, only employers with 50 or more workers are required to guarantee a job.

State Sen. Hannah-Beth Jackson (D-Santa Barbara), the bill’s sponsor, said state law hasn’t kept up with the desire among parents to bond with their new children.

“More and more moms are in the workplace, and more dads are wanting to be involved with their children,” she told Rewire. “Many of our policies have remained frozen in time.”

New fathers accounted for nearly 36 percent of the 249,293 most recent parental leave claims, according to the state Economic Development Department. Paid parental leave is associated with a host of benefits, including lower infant mortality and improved maternal and child health outcomes. Leave taking by fathers was found to promote gender equity and increase fathers’ involvement with children, which is associated with greater language skills and improved cognitive and social development.

SB 63 cleared the state senate, and is set for a hearing Wednesday in the state assembly’s Labor Committee.

California was the first state to enact paid family leave, but it now trails other states in offering job protections. If the bill becomes law, California would join Rhode Island and New York in providing job-protected paid family leave.

The legislation’s backers include nearly 70 work-and-family and health advocacy groups, including the American Academy of Pediatrics, California Medical Association, and First Five California. Dozens of industry groups, such as the California Chamber of Commerce, oppose the legislation, suggesting it’s a “job killer.” California’s governor last year vetoed a nearly identical bill authored by Jackson. Jackson told Rewire she has made overtures to the governor’s office and listened to his staff’s concerns.

“The bottom line is it’s time for our parental leave policies to reflect the realities of working families in the 21st century,” she said.