"You've reached a moment where the dollar strength is turning to have a feedback loop back on Fed policy which in returns feeds back onto the dollar," said Alan Ruskin, head of G-10 currency strategy at Deutsche Bank. "I still think if the economy is robust enough the Fed will tighten in June. Where it's more convincing is the path of future tightening is not nearly as stiff as it would be if the dollar was weak." Ruskin expects euro-dollar parity at the end of the year.
The greenback has moved sharply higher this year on the prospect of higher rates and a stronger economy, but also because the euro has weakened as Europe's central bank eases in the face of Fed tightening. The euro was trading at $1.06 Thursday after bouncing near $1.10 Wednesday. Now, the slower trajectory of Fed rate hikes could slow the dollar's rally.
Read MoreThis chart say euro could plunge another 30%: Top technician
Dan Katzive, head of North American foreign exchange strategy at BNP, explained some of the dollar's big move this week. "I think you have to think big picture. Bullish dollar is a very high-consensus view and what that means is if you get a big pullback there's a reservoir of momentum from people that haven't been able to get in at a good level," he said. "That's why I think you didn't stay long at those cheaper dollar levels." Katzive said he expects the dollar to trade differently, now that the Fed noted its impact.
"It makes it harder to have a one-way momentum trade in the dollar," he said.
The Fed tweaked the language in its statement to show it is getting closer to launching its first rate rise in more than nine years, but Fed Chair Janet Yellen said while June is possible for the first hike, the central bank could take its time. The dollar initially reacted to the Fed's projection for a slower path of rate increases, including expectations for a year-end fed funds rate, now projected at half the 1.125 percent it initially forecast for the end of this year.
"I don't think it changed the broader dynamic. There's a presumption in some places that the Fed gave signal that would have pushed out the likely timing of a rate hike, in part because of the strength of the dollar," said Ruskin. "I'm not convinced. If we print strong payroll numbers before the FOMC in June, I think June is still very likely."
Rick Rieder, BlackRock's co-head of Americas fixed income, said he thinks June is still a possible but the base case has become September. "When the economy and the markets give you a window to move, missing the window can be dangerous. But clearly they're going to be deliberate in their path. We think for the time being we're in the low-rate range for a long time," he said.
Rieder said he expects the high yield on the 10-year Treasury this year to be about 2.25/2.50 percent, and he expects a flattening trade when the Fed starts moving. That would be where the short end of the curve—two-year to five-year notes—see yields rise at a faster pace, closer to the longer end.
Read MoreThe trillion-dollar question: Allianz Global CEO
Never before have the markets been so fixated on and influenced by central bank policy, and that's a formula for more volatile trading, Rieder said. "You have a world that's driven by excessive monetary policy. ... What happens is everything moves together based on where policy's next move is. When it moves one way or the other, everyone wants to follow it because it's so big. You have this phenomena of everything moving all one way at the same time," he said.
Rieder said that includes traders positioning around other central bank's policy, such as the bond-buying program launched by the European Central Bank.
Michael Materasso, senior vice president and co-chair of Franklin Templeton's fixed income policy committee, also expects to see the curve continue to flatten, in part as foreign buyers dip into the longer end. The U.S. 10-year, for instance, is relatively more attractive to some investors with a yield of 1.96 versus the low 0.15 percent yield on the German 10-year bund.
"We think that would be because of proactive Fed policy and the technical effect of QE from the ECB and Japan where funds will be flowing into the U.S.," Materasso said. The question is though whether it will be a bear flattening where rates rise across the curve but less in the 10-year and 30-year or will the short end rise up to meet the longer end.
"It's too early to tell but I think the trend of a flattening yield curve happens because of a proactive Fed; relatively low interest rate environment; and buying coming from Japan and Europe," he said.
Materasso said the Fed will do all it can to keep the markets calm. "My assumption is even when they raise rates for the first time, unless this economy is going to take off like no one believes in the second half of the year, I would assume with the first rate hike they will state that zero interest rate policy is no longer appropriate," he said, adding the central bank would emphasize the path of rate increases will be gradual. "They're going to soften the blow."
But those expectations for continued low Treasury yields are encouraging for stock investors, who were initially cheered by the Fed's slower rate increases.
After Wednesday's surge, stocks were mixed Thursday, with the Dow down 117 at 17,959 and the S&P 500 off 10 at 2,089. But small caps and the Nasdaq were winners, with the Nasdaq finishing at 4,992, up 9. The small-cap Russell 2000 rose 2 to 1,254, just below its all-time high.
Read MoreBoone Pickens: Why I see $70 oil by year's end
"The only way to justify a fair value on equities is to look at them through the lens of bonds," said Jack Ablin, CIO at BMO Private Bank. Low rates make stocks appealing, but "by every other measure they seem stretched." Ablin has been directing more funds to foreign stocks.
Ablin said the Fed's posture could make stocks more volatile. "Every month that the Fed doesn't tighten is going to make equity valuations that much more stretched. That makes the Fed that much more important in deciding whether to own equities, which will make them remarkably volatile. It's like a worldwide game of chicken. That's my concern," Ablin said.
Peter Boockvar, chief market strategist at Lindsey Group, said the test for stocks will be earnings season, expected to get underway in early April.
"The difference this time versus the last couple of years when you had QE (quantitative easing) and zero interest rates, you also had strong earnings," he said. "Now you have no QE. You have zero interest rates, but you no longer have strong earnings growth."
Read MoreYardeni: Markets all rigged, it is what it is
Boockvar said earnings are expected to grow only by about 2.5 percent this year. The strengthening dollar has sent chills through the stock market recently as traders worry it will dent foreign earnings of multinationals. The dollar index is up nearly 10 percent so far this year.