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Cars drive on Fulton Street in San Francisco in the summer of 2015. Businesses there oppose a new measure on extended paid parental leave expected to be signed into law in April 2016. Getty Images

The San Francisco board of supervisors' recent move to require employers to offer extended paid parental leave was welcomed by mothers, fathers and advocates Tuesday. But one group was pushing back against the new policy: business owners.

City entrepreneurs argued that the rule, which Mayor Ed Lee is expected to soon sign, would simply cost too much to implement. The measure would force business owners who have 20 employees or more to give new parents six weeks of paid time off, the Associated Press reported.

“The message you have to send sometimes, is 'Hey, enough is enough,'” Mark Dwight of Rickshaw Bags, a messenger bag retailer, told KPIX. “It’s this constant piling on. It’s the death of a thousand cuts."

Businesses are not fronting the full cost. The state covers about half of employees' wages for parental leave under the program California's Paid Family Leave. But business owners said their stress was skyrocketing, in part because they're also dealing with a 2014 mandate to raise the minimum wage to $15. California Gov. Jerry Brown signed a similar bill into law Monday for the state.

"They don't necessarily have the resources, they can't absorb the increases in cost, and they feel like it's kind of relentless, it's one thing after the next," Dee Dee Workman, the vice president of public policy at the San Francisco Chamber of Commerce, told the AP.

Proponents of paid family leave say it has a host of benefits, among them improved mental health, longer periods of breastfeeding, higher wages and increased productivity when parents return to work. The city's small business commission, however, was nearly unanimously opposed to San Francisco's new policy. It voted 6-1 to urge the board of supervisors to shut down the measure.

“Can we make the board of supervisors run a business, meet payroll, so they understand how these things work?” Commissioner Stephen Adams told the San Francisco Examiner. “Enough is enough is enough. This is bad for small business.”

If Lee signs the measure, businesses will have to start complying in July 2017 or January 2018, depending on how many employees they have.