The Fed's dual mandate is very important here. And there's some movement toward "automatic QE in case unemployment starts to rise" - https://www.stitcher.com/show/voxs-the-weeds/episode/fix-rec... (Matt Yglesias wonktalks with Claudia Sahm, very recommended)

CPI is very important, but the labor numbers are much better (since they are easier to measure), so CPI might become a secondary (high level, target) metric over time.