"I think what the market wants to know is, 'What happened?' What happened in the course of a few weeks?" Krosby said.
"Does 38,000 jobs [in May] bother her when she said one month doesn't make a trend? Don't think for a minute the market doesn't make its own assessment. In many ways, Janet Yellen basically acquiesced to the market, because the market said, 'You're not moving anything,'" Krosby said.
U.S. Treasury yields continued to edge higher Monday in a recovery from last week's lows. The 10-year yield held near 1.67 percent, still close to lows seen during the stock market correction earlier this year when recession concerns worried markets.
"I don't think the Fed's inconsistent. I don't think they've lost credibility," Allianz Chief Economic Advisor Mohamed El-Erian said at a press briefing Monday. "But if you're data-dependent, you're going to look inconsistent."
Federal Reserve Governor Jerome Powell is scheduled Tuesday afternoon to give opening remarks at a New York roundtable on the interim report of the Alternative Reference Rates Committee.
No major economic data is expected, but some key earnings reports will be in focus for their perspective on economic growth. Earnings due before the bell include CarMax and Lennar. FedEx, KB Home and Adobe Systems are scheduled to report after the close Tuesday.