Traders are roughly divided on whether the Federal Reserve will hike rates next month. Today's CPI report could significantly shift those expectations.

A softer-than-expected print today "would all but rule out a September hike," write Bank of America strategists led by Alex Cohen in a note today. It would also "notably challenge" expectations that officials will lift interest rates by a quarter-percentage point before the end of the year.

Conversely, a hotter-than-expected report should put a September hike in play, they wrote. However, "the decision would still likely hinge on August data, given Chair Warsh's apparent reluctance to hike."