"They kind of struck a balance between acknowledging there may have been some transitory factors in a slow Q1 and modestly upbeat about going forward," said Ward McCarthy, chief financial economist at Jefferies. "They didn't tip their hand in either direction."
First-quarter GDP growth was reported Wednesday at 0.2 percent, much lower than the 1 percent expected. Stocks sank and the dollar was slammed after the GDP data, with the euro up more than 1 percent against the dollar.
"Sometimes you get a trend day after Fed day, but I don't think tomorrow will give us a bit more of a clear-cut story," said Scott Redler of T3Live.com. "If we break below 2,090/2,094 (on the S&P 500), we could see pressure."
Besides the personal income and spending data, there are weekly jobless claims and the employment cost index for the first quarter, both released at 8:30 a.m. Chicago PMI is released at 9:45 a.m.
Read MoreDollar trounced on GDP, view of easy Fed
"This (Fed statement) doesn't move the needle much one way or the other," said John Briggs, head of strategy at RBS. "It's a place holder."
The markets are betting that a Fed rate hike could happen in September but are only giving about a 48 percent chance to a quarter-point hike by then, according to Briggs. He said market odds are much higher for December – with a more than 100 percent chance of a rate hike then, according to RBS calculations.
The Fed's dual mandate makes improvements in labor and inflation critical factors in its thinking on interest rates. "They need to see some evidence that inflation is moving higher or wage costs are moving higher," said Joseph LaVorgna, chief U.S. economist at Deutsche Bank. "If oil prices stay where they are or gradually move higher, that makes it easier for the Fed to hike."
LaVorgna said the absolute number of jobs added is not going to be what moves the Fed. "If ECI comes out stronger than expected, and the next average hourly earnings reports are better than expected, that to me is more important than whether you get incremental improvement in the jobs market. I don't think this is about labor per se, it's about finding that trigger for wage and price trends that clearly tells the fed we've been too easy for too long," said LaVorgna.
LaVorgna expects to see nonfarm payrolls at 225,000 next week, but the consensus so far is slightly lower. As for Thursday's data, he expects the PCE deflator to be up 0.1 percent, income up 0.2 percent and consumption, up 0.4 percent.
Read MoreUS Treasury yields whipsaw after Fed statement release
After the Fed statement Wednesday afternoon, the bond market attempted to rally but it failed. The 10-year was yielding about 2.04 percent in late afternoon trading.
"Q1 is weak. April has started to be disappointing," said David Ader, chief Treasury strategist at CRT Capital. "The market is telling me that's enough, now we need to see what Q2 looks like."
Ader said none of the data between now and the nonfarm payrolls next Friday will help clarify the picture, with April's jobs report the first monthly employment report for the second quarter.
Chris Rupkey, chief financial economist at Bank of Tokyo-Mitsubishi said the Fed could still raise rates in June, even with the weak data. "We think June is in play for the simple reason the data, the next two monthly employment reports due May 8 and June 5 could show the 5.5 percent unemployment rate today will be close enough to the Committee's 5.0-5.2 percent full employment finish line for the Fed to start to raise rates finally. It all comes down to the data. There is nothing in the statement ruling in a rate hike or ruling it out. It depends on the data, it depends on unemployment, that's the bottom line," he said in a note.