Does raising the minimum wage...

...lead to slower job growth? Not necessarily. From Bloomberg, "Highest Minimum-Wage State Washington Beats U.S. Job Growth" (my emphasis):

When Washington residents voted in 1998 to raise the state’s minimum wage and link it to the cost of living, opponents warned the measure would be a job-killer. The prediction hasn’t been borne out.

In the 15 years that followed, the state’s minimum wage climbed to $9.32 -- the highest in the country. Meanwhile job growth continued at an average 0.8 percent annual pace, 0.3 percentage point above the national rate. Payrolls at Washington’s restaurants and bars, portrayed as particularly vulnerable to higher wage costs, expanded by 21 percent. Poverty has trailed the U.S. level for at least seven years.