Well, this is interesting. From the Los Angeles Times:

The campaign to push Los Angeles County to significantly raise the minimum wage suffered an unexpected setback Tuesday, with a key county supervisor demanding a postponement to address complaints from small-business owners.
Labor unions and other supporters had been lobbying the Los Angeles County Board of Supervisors to follow the Los Angeles City Council and boost the minimum wage in unincorporated areas to $15 an hour in five years for large businesses and six years for those with fewer than 26 employees. They hoped the county’s support would prompt other local cities to follow suit, leaving L.A. less isolated with its higher wages.
The swing vote on the plan is Supervisor Hilda Solis, a Democrat, union ally and former U.S. Secretary of Labor in the Obama administration. Solis asked for the delay after hearing complaints from constituents. County officials and labor leaders still expect the Board of Supervisors to approve the hike.
But Solis’ hesitation spotlights the conflicting political forces she must balance in addressing the issue.
She was elected last year with heavy support from unions backing the wage increase, as well as endorsements from major business groups that have opposed it. Along with two other Democratic supervisors, Sheila Kuehl, who proposed the wage increase, and Mark Ridley-Thomas, Solis makes up a new labor-allied majority on the five-member board.
But Solis joined Don Knabe and Michael Antonovich, the two Republicans on the five-member county board, Tuesday in raising questions about how the increase would affect businesses, particularly smaller enterprises.
“I care very deeply about what happens to those mom and pop businesses and nonprofits,” she said. […]
Solis reiterated Tuesday she wants to raise the minimum wage. But she said the county lacks adequate information on the effects the current proposal would have on small commercial enterprises in county-controlled areas. She also called for county officials to develop a broad plan to assist businesses transitioning to higher wages, including streamlining the permitting process and offering training to workers.

(Bold mine.)