An unusually public rift between the Fed chair and two governors is adding to an already confused policy message that has been hurting the central bank's credibility with markets.

Traders are watching for some clarity in the message Thursday from New York Fed President William Dudley, seen as one of those closest in view to Fed Chair Janet Yellen. He speaks at Brookings at 10:30 a.m. ET, on the topic of "Fed at a crossroads."