Now that the Fed has spoken, traders are looking to Thursday's CPI inflation data for clues as to its next move.
The consumer price index is expected to be up 0.5 percent in May, compared to 0.1 percent in April. Without food and energy, CPI is projected to rise 0.2 percent, compared with a surprise 0.3 percent in April, for a year-over-year pace of 1.8 percent.
The Fed on Wednesday left rates unchanged after its two-day meeting, but it did provide a statement and forecasts that suggest it could raise rates once, if not twice, this year should it see improvement in economic data, including inflation.
The central bank's chair, Janet Yellen, in a post-meeting briefing, said the economy and specifically inflation, have not met the conditions required for a rate hike. But she said most Fed officials see a rate increase this year and they expect the data to improve.
"I think that's the Fed's trigger now. That's what they're looking at as far as how they're going to time their normalization of rates. That's the one aspect of the economy that's keeping them from the liftoff hike," said Ian Lyngen, senior Treasury strategist at CRT Capital.
"If we get a trend higher in inflation, that would be an indicator that they are going to be more comfortable. If we get a high CPI tomorrow, people are going to move solidly to September rate expectations versus December, and that's going to be bearish for the front end of the curve."
However after the Fed's statement Wednesday, buyers moved into the front end of the Treasury curve, and yields fell along the curve with the exception of the 30-year bond. Lower rates are more indicative of market expectations for Fed rate hikes.
Read MoreFed leaves interest rates unchanged
"The market trades like there were more expectations that the Fed would indicate more of a September lean" toward a rate rise, said John Briggs, head of strategy at RBS.
The central bank would like to see a 2 percent inflation rate, and its preferred inflation measure, the PCE deflator, is running at a clip of just 1.3 percent. That contrasts with the 1.8 percent year-over-year gain in CPI.
Deutsche Bank's chief U.S. economist, Joseph LaVorgna, said the difference between the performance of CPI and PCE is in part a divergence in how medical costs are calculated in the two indexes. CPI, measuring prices charged to consumers, showed a 0.7 percent rise in April for medical costs, or a 3 percent year-to-date gain. Meanwhile, he said the medical costs in the PCE, which represent revenues for providers, are up only 0.1 percent year to date.
Read MoreHey, Fed—Wake me up when September ends
LaVorgna said he believes the acceleration in CPI will continue. For one, shelter costs are 40 percent of the core CPI and with a vacancy rate at a 22-year low, costs are likely to rise faster than their current 3 percent year-over-year rate, he noted.
"If we get a high number tomorrow the market will react," said LaVorgna.
"If the CPI surprises to the upside, and we establish another month with this kind of a 0.2 kind of trend, one has to be reasonably comfortable that PCE will approach it over time ... I'd be surprised if a year from now, we were anywhere near as low on the core PCE deflator," said LaVorgna. "Inflation is a function of something that happened much earlier. I think we put too much weight on some of these temporary factors like the dollar and energy."
"It seems to me CPI is conceptually easier to measure and is more intuitive," said LaVorgna.
What to watch
CPI is expected at 8:30 a.m. ET.
Weekly jobless claims are reported at 8:30 a.m.
The first-quarter current account is due at 830 a.m.
Philadelphia Fed survey is released at 10 a.m.