Scott Clemons, Chief Investment Strategist at Brown Brothers Harriman, said he is watching inflation but the single most important data he is watching is the average hourly earnings growth, at about 2.5 percent. "That may be the source of inflation pressure that forces the Fed's hand, but not yet. Wages are beginning to outpace core prices," he said.
Core CPI has been above the Fed's 2 percent target, but the Fed's preferred inflation measure is the PCE deflator, and it is below 2 percent.
Clemons said the Fed's change in interest rate forecasts is not a surprise. "I think the consensus has been moving that way for some time. You have one more rate hike [this year], and then it just becomes a guessing game," he said.
But McCarthy said what seems to be an about-face by the Fed in its longer-term view is bad for confidence.
"They shatter confidence. What comes across is they're not confident in the economy and they're not confident in monetary policy, and that's not a good thing from a central bank," said McCarthy.
Besides CPI, weekly jobless claims are also reported at 8:30 a.m. EDT and are expected to rise slightly to 270,000. The current account is also reported at 8:30 a.m., and the Philadelphia Fed survey is released at 10 a.m.
Caron said he was also watching the Bank of Japan overnight, which he said has a 50 percent chance of surprising the market after its meeting.
Amherst Pierpont chief economist Stephen Stanley expects to see a 0.3 percent increase in CPI, and 0.2 percent in core. "A noticeable seasonally adjusted rise in energy prices drives the headline estimate, while my core forecast reflects a largely trend-like performance. Core services prices have firmed slightly and will continue to drive the aggregate, led by shelter costs. Over time, core goods prices are likely to stabilize or tick up in the wake of the turnaround in import prices in recent months, but it is likely too early to see that effect by May," he wrote.