A dovish Fed managed to reverse some market perceptions that it would be more aggressive with rate hikes and spun the onus back to the performance of the economy and whether recent sluggishness is just the result of bad winter weather.
Next up on the economy is Thursday's weekly jobless claims, expected at about 320,000, off slightly from 326,000 last week. There are also import prices released at 8:30 a.m. ET, and retailers report monthly chain store sales.
Stocks rocketed and bonds rallied Wednesday at the shorter end of the curve, as traders viewed the Fed's minutes from its March 19 meeting as a sign the Fed would keep its easy rate policy in place for a long time even as it unwinds its bond-buying program. On Thursday morning, stock futures were lower ahead of the open, but the move lower in Treasury yields continued.
"The market's saying they were dovish. The initial reaction (to the meeting) was hawkishness," said John Canally, investment strategist and economist with LPL Financial. "We're now back to focusing on the data. The other key out of this was a large chunk of them said it was the weather. The question came up. Is it the weather? Is it something else? This clearly says it was weather."
Traders focused on a key section of the minutes, where the Fed discussed its members' targets for the fed funds rates and how it worried about misleading the markets with its forecast. The Fed literally presents its forecasts with dots, representing each members view on a chart.
In the minutes, the Fed noted: "A number of participants noted the overall upward shift since December in participants' projections of the federal funds rate included in the March (projections), with some expressing concern that this component of the (projections) could be misconstrued as indicating a move by the Committee to a less accommodative reaction function."
Deutsche Bank's chief U.S. economist, Joseph LaVorgna, said the expectation for the fed funds rate after the March meeting went from a rate of 0.75 percent in the second half of 2015 to 1 percent, and from 1.75 to 2.25 percent in 2016. "That was based on a combination of the new forecasts as well as her six months comment," he said.
Fed Chair Janet Yellen, in her first post-Federal Open Market Committee press briefing, rocked the markets that day by saying the Fed could move to raise the fed funds rate six months after it ends its bond-buying program.
That drove yields sharply higher in the two-year and five-year part of the Treasury curve, as markets braced for a more aggressive Fed than had been expected. Those yields reversed course sharply after the Fed minutes Wednesday—falling to levels they were trading at before the March 19 meeting. The five year was yielding 1.62 percent after the 2 p.m. ET minutes release, off from its high of the day of 1.71 percent.
On Thursday, the five-year was at 1.60 percent.
"Now the bond market is saying: 'We get it. You're not going to raise rates quickly in the future, so over a five-year time period, rates shouldn't be this high," said George Goncalves, head of rate strategy at Nomura Americas. The 10-year yield barely budged after the minutes, trading at 2.69 percent, just slightly lower but in the middle of a range it was in all day.
On Wednesday, the yield on the two-year retraced the gains it made since March 19, and fell back to as low as 0.30 percent and was trading at the 0.35 percent level late in the day, still well below its session high of 0.42. The two-year yield had jumped to 0.43 percent on March 19 from 0.35 earlier that day.
The , which has been most beaten down lately, led the market gains Wednesday, jumping 1.7 percent to 4,183. The Dow had its best day in more than three months, climbing 181 points to 16,437. The S&P 500 rose 20 points to 1,872.
One of the market's worst fears is that the Fed will cut back on its easy money policies at a time when the economy is just not growing fast enough to counterbalance it. The FOMC tapered back another $10 billion at its March meeting, while slightly downgrading its economic forecast to growth of 2.8 to 3 percent this year, down from 2.8 to 3.2 percent.
"Most people are banking on this is the weather, a soft patch and we'll get through spring, and it's off to the races," said Goncalves. "Even though the market trades well, people are inclined to hate the bond market than like it, especially this year when there were such high hopes that we'd see a recovery. I don't think people are willing to throw away that theme so quickly."
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Goncalves said if the Fed members were questioning their own rate guidance, they could also be questioning their own guidance on the economy.
But LaVorgna said the Fed may be too negative, and policy will be dictated by the economy's strength. He expects second-quarter growth of 4.2 percent, up from 2 percent in the first quarter.
Read MoreStock market reactions to Fed minutes releases
"The Fed has over-engineered monetary policy. The message is getting garbled, and we're one big employment report away, as we've been for a while, from the market totally throwing this minutes out the door and the Fed changing its tune, at least on the margin," he said.
Fed minutes have more recently than not been read as hawkish, as they also represent the views of some of the noncore members of the Fed. But these minutes were not viewed that way, and some questioned whether the Fed fashioned them after the fact to influence the market.
"Clearly, Janet Yellen and the other doves on the Committee were startled by the market reaction to the March 19 statement (and her "6 months" gaffe) and decided that the minutes needed to push back against that market move. I have not traditionally been a big conspiracy theorist with regard to the Minutes. I had believed that the Minutes were generally a straightforward recount of the FOMC discussion, but in this case, the Minutes appear to have been crafted after the fact with an eye toward unwinding the perceived change in the policy outlook that took place on March 19," wrote Stephen Stanley, chief economist at Pierpont Securities.
Chris Rupkey, chief financial economist at Bank of Tokyo-Mitsubishi, questioned the comment about the fed funds rate targets.
"It certainly looks like a duck the upward shift in the dots, even if it doesn't talk like one. The median forecast for year-end 2016 was 1.75 percent in December and it moved to 2.25 percent in March. It's up 50 bps, that's a fact," he wrote in a note.
"One thing is certain, Fed policy is not as easy to interpret as we thought, and you can't just follow the dots," he added. "The minutes may even have been written to push back on the markets interpretation from the March meeting statement that change is in the air. Our view is that the March meeting was important and change is coming for Fed policy as it has become less and less convincing that there is a great deal of slack remaining in the economy five years after the recession ended. The March meeting minutes are stale anyway as we just got Friday's jobs report 192K jobs in March with 37K of upward revisions. The economy is better than the Fed thinks. And the jobs report hammers the point home."
—By CNBC's Patti Domm.