After February's surprisingly strong jobs report, the Fed is now even more likely to send a strong signal at its March meeting that a rate hike is near, and more traders are now speculating on the first move in June.
But a number of economists say the central bank is still likely to hold off in June, and move to raise rates in September or even later because of the lack of wage growth and inflation.
Nonfarm payrolls for February totaled 295,000, more than 50,000 above economists' consensus, and the unemployment rate fell to 5.5 percent, from 5.7 percent. Average hourly wages crept up less than expected—at just 0.1 percent, after a surprise gain of 0.5 percent in January and a decline in December.
Read MoreJobs creation jumps despite tough weather
Treasury yields rose Friday and stocks sank as traders reacted to the strong labor report and its potential to pull the Fed off the sidelines. The 10-year yield, at 2.08 early in the day, rose to 2.23 percent. The two-year yield was at a 2015 high of 0.72 percent, from less than 0.60 early in the day.
"I think a 5.5 percent unemployment rate clinches a June rate hike, which means 'patient' comes out (of the statement) in a week and a half," said Peter Boockvar of The Lindsey Group.
The word "patient" in the Fed's statement has become a point of debate, since its chair, Janet Yellen, said in congressional testimony that removal of the word would be a precursor to a rate hike. Economists say there is a good chance the central bank will drop the word when it meets March 18.
"We're cranking out jobs hand over fist. We shifted to a higher gear in November, and we're still going," said Ward McCarthy, chief financial economist at Jefferies. "The weather had little effect on this in terms of jobs growth. The missing piece continues to be any evidence at all of upward pressure on wages. The Fed must be delighted. We're pounding out the jobs, but at the same time, the lack of wage growth must be frustrating to them."
Read MoreCommentary: Rate hike in June?
Economists had expected a weather effect, but there were few signs of it except for a dip in hours worked. The February report showed gains for workers in food service and drinking establishments of 59,000, professional and business services of 51,000 and construction jobs of 29,000. Mining, which includes energy, fell by 9,000 jobs as the sector was hit by lower oil prices.
The 295,000 jobs in February follow a revised 239,000 for January, moved lower by nearly 20,000. But job growth for December remained unchanged at 329,000.
Deutsche Bank's chief U.S. economist, Joseph LaVorgna, unlike other economists, had not expected a weather impact in the February report. He also does not necessarily anticipate the Fed to wait for average hourly earnings to turn higher.
"There's a lot of time between now and June. The earnings could be soft, but that doesn't mean the ECI (employment cost index) and other data won't continue to trend higher," he said.
LaVorgna said the Fed could be viewed as being behind the curve if it doesn't act sooner rather than later. "You have to really be sensitive to any sign that inflation is turning. This is the problem with waiting," he said. "The trends are there. It's absurd to think a mild hike or two is going to derail the economy. That's the key thing. For symbolism purpose alone, it makes sense. If they move rates, they then have the flexibility to wait (for further increases)."
Mesirow Financial's chief economist, Diane Swonk, said elements of the jobs report were fairly well-balanced in terms of their influence on Fed policy. "I think it generally is balanced, but the wages are what the doves will stick on and at the end of the day, it's inflation that matters." she said.
"It's still not perfect, and we're still playing catch up and that's what the Fed wants. ... It's going to be difficult on inflation when you don't have wages. It doesn't mean they don't remove 'patience.' They have to remove 'patience' and say it's data driven, which means inflation has to firm," she said.
Jan Hatzius, chief economist at Goldman Sachs, said the inflation metric may ultimately be the most important to the Fed. "I think you can make both sides of that argument. I lean toward the side that it would be better to wait longer," he said. "My expectation is that they come out somewhere in the middle and ultimately liftoff in September."
But JPMorgan economists disagree, and they see a June rate hike.
Read MoreStrong jobs just reset Fed rate clock: Jim Paulsen
"The only blemish in the report was the anemic 0.1 percent increase in average hourly earnings, which left year-ago wage growth subdued at 2.0 percent," wrote the firm's chief U.S. economist, Michael Feroli.
The Fed wants to see wage growth rising above 3 percent.
"Even so, we think today's report reinforces the case for a Fed liftoff in June and makes the removal of 'patient' in the March statement a near-certainty, in our opinion. The decline in the unemployment rate to the top of the Committee's central tendency estimate of the natural rate of unemployment should instill 'reasonable confidence' among the FOMC that inflation one to two years ahead will be moving higher," he wrote.
Feroli also noted that San Francisco Fed President John Williams, a noted dove, pointed out that "wages lag the cycle, and slack is more helpful when thinking about the medium-run inflation forecast."