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An improving economy could force the Fed to shift into rate hiking gear sooner than it would like, some Fed watchers say.
While a move to higher rates sooner is not a majority view, it is one that has been picking up momentum. Others see the Fed holding off on rate hikes until late next year, but then hiking much more aggressively than expected.
The Fed meets for two days, starting Tuesday, and is widely expected to taper back its monthly bond buying program by another $10 billion to $25 billion—and do little else.
"They've got to decide how they're going to raise rates, when they raise rates. That's what the bulk of their talk has to be about. The minutes are going to be revealing, more and more. They've got to hash this out," said Mesirow Financial chief economist Diane Swonk. Raising interest on excess reserves and reverse repos are tools that are likely to be used by the Fed. "Bottom line, if the economy is good enough, they'll raise rates."
While the Fed is not likely to reveal any more about the timing of rate hikes or how it will unwind its more than $4 trillion balance, Fed officials are likely to discuss those topics at this week 's meeting. After this week, it next meets Sept. 16.
Traders are watching for clues on Fed timing in its statement, particularly around the Fed's dual mandates of helping employment and fighting inflation. It last said unemployment "remains elevated," and described inflation as running below its objective of 2 percent.
The Fed has said it would end the bond buying program in October, so it is likely the talk will turn to post-tapering actions, like when the Fed could end its policy of reinvesting the proceeds as the securities within its portfolio mature.
Economists expect the Fed's more hawkish members to ramp up their calls for ending easy policy, if economic data improves. Friday's July employment report is expected to be an important metric for the Fed, as is the personal consumption expenditures (PCE) inflation reading, due the same day.
"Knowing (Fed Chair) Janet Yellen, she'll wait until March, but I think pressure is really growing to do something in January. Whereas the market doesn't think this happens until the middle of next year, and all the economists at the big firms don't think it's happening until the third quarter," said Peter Boockvar, chief market analyst at the Lindsey Group.
Read MoreOpinion: Fed officials in denial
Already a hawkish corner of the Fed is seeking an earlier move to "normalize" policy. St. Louis Fed President James Bullard predicts the Fed could start raising rates in the first quarter of 2015, well ahead of most of his colleagues. And in an unusual and high profile commentary just ahead of the Fed meeting, Dallas Fed President Richard Fisher wrote in The Wall Street Journal this weekend that the Fed is risking keeping policy "too loose, too long."
Taken from a speech earlier in the month, Fisher made the point that the Fed is creating financial excess that could lead to financial instability. He also said the economy is reaching "the desired destination faster than we imagined."
"Maybe it's his way of saying he's going to dissent," said Boockvar, adding he thought Fed officials would be in a quiet period ahead of the meeting.
Swonk said she expects the Fed to hold off rate hikes until the end of 2015, in part because there are no signs of wage pressure. Some parts of the economy appear to be improving but there are still signs of trouble in the detail.
For example, while hiring is improving and the unemployment rate is dropping, the participation rate, which measures people in the work force or who want to be in work force, is still at a post-recession low.
That is also a metric that Yellen watches closely. "The hawks are going to start squawking a lot more this fall, and you will see defense about the repurchase program and timing on when the Fed raises rates," Swonk said.
"Next year, it's a much more dovish Fed," said Swonk, adding she expects Yellen and the dovish core of the Fed to prevail.
"We know the outcome of the Fed meeting. It's steady as she goes," Swonk said.
BlackRock's Rick Rieder, co-head of America's fixed income, has said the Fed may need to move sooner than many market watchers expect because low rates may actually be holding back economic growth and job creation.
UBS economist Drew Matus said the Fed should have begun to tighten policy a while ago, and while he doesn't expect it to move sooner, he does see it having to raise rates faster once it begins.
"By any measure, using the Fed's own forecasts for growth and inflation and unemployment and inflation, they are behind the curve, even as we speak," he said in an interview with CNBC's Steve Liesman. "So even though we are looking forward to a taper, and that's moving in the right direction, certain policy rules, like John Taylor ascribed to or created, really suggests the Fed should have gone a while ago."
Jefferies chief financial economist Ward McCarthy said he expects the Fed to actually move later than expected, because its policy moves have been very slow and cautious. But once they start hiking, he agrees with Matus that it will be more aggressive than expected.
As for this week's meeting: "One, they'll taper $10 billion. Two, I think in the balance sheet guidance they'll confirm from the discussion from the minutes…about making the last tapering in October, and I think in their discussion of the economy, they will be cautiously optimistic but still include the caveats about the housing sector and labor market slack," he said.
Besides the concerns the Fed has stayed easy for too long, there are the opposite fears that it is unwinding easing before the economy has picked up real traction, and that higher rates could harm critical parts of the economy, like housing.
The economy is still growing at a sluggish speed. That should show up Wednesday when second-quarter GDP is released, and economists are forecasting growth of just 2.9 percent. At that pace, it does not show much spring back from the 2.9 percent contraction in the first quarter.
Read MoreQ2 growth shrinking again
Fed watchers are looking as much to the data this week as the Fed statement for clues on its policy path. The July employment report on Friday, is expected to show the economy added more than 200,000 jobs for a sixth month, and the unemployment rate is expected to drop to 6 percent. The Fed has stepped back from its target of 6 percent unemployment as a pivot point for considering rate hikes, but the market remains fixated on the number.
Tuesday's data includes S&P/Case-Shiller home prices data at 9 a.m. ET, and consumer confidence at 10 a.m.
The Fed has a target of 6 to 6.1 unemployment for this year, and it sees it at 5.4 to 5.7 percent next year. It expects inflation next year of 1.5 to 2 percent. "They can meet their year-end 2015 targets by the end of this year," said Boockvar.
Boockvar said the soft demand at the $29 billion 2-year auction was symptomatic of the market's expectation that the Fed will be pushed to hike. The yield was 0.544 percent, the highest yield at auction since May 2011. Treasury auctions $35 billion in 5-year notes Tuesday.
"I just think the bond market is beginning to think the Fed is falling behind the curve…even though I hate that cliché," he said.
Besides the Fed and data, market focus will be on the dozen of earnings reports expected Tuesday. Early morning reports are expected from Merck , Pfizer, UPS, Aetna, Corning, Deutsche Bank and BP. American Express, Twitter, Amgen, Anadarko Petroleum and Dreamworks report after the closing bell.
—By CNBC's Patti Domm.