This is the Fed's biggest economic headache

If investors learned anything from Fed Chair Janet Yellen's testimony to Congress this week, it's that the central bank is willing to wait for inflation to catch up to employment before hiking rates.

It could be a long wait—longer, in fact, than many market participants anticipate.

Language tweaks in Yellen's semiannual appearance Tuesday and Wednesday sent strong indications that even if the Fed removes the word "patient" from its next post-meeting communique, it will remain, indeed, patient when it comes to rate hikes.

"The more I think about it, the more I feel that Yellen was very dovish," David Rosenberg, economist and strategist at Gluskin Sheff, wrote of the testimony. "If a shift in policy was coming, this was the setting for verbalizing it—she passed up the opportunity."

Janet Yellen
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Janet Yellen

At the core of the central bank's hesitancy is that despite substantial improvements in benchmark employment measures, inflation remains well below the Fed's targeted level of 2 percent.

Read MoreDudley: Why Fed may need to get 'more aggressive'

Even as job creation continues to grow, little in the way of wage pressures have followed. Falling gas prices and disinflationary conditions around the globe also are helping mute pressures on the Fed to normalize crisis-level monetary policy.

"What is really key is that for the first time, she linked rate increases to both the performance of the labor market and to being convinced inflation will rise toward 2 percent," Rosenberg added. "Yellen is bullish on growth and yet shows no signs of moving off zero."

Since lowering its target funds rate to near zero in late 2008 and embarking on a bond-buying program that swelled its balance sheet to $4.5 trillion, the Fed's efforts to use monetary policy to spark growth have met mixed results. Stock market values have soared to new highs and the unemployment rate has fallen—thanks at least in some part to generational lows in labor force participation—from a crisis-era 10 percent to the current 5.7 percent.

However, inflation as counted through the Fed's preferred measures has remained low other than flare-ups in food and energy that policy markers consider "transitory." Gross domestic product also has been lackluster, with 2014 registering an annualized 2.4 percent gain.

In a perfect world, declining unemployment would be met with higher wages and price stability, which would help the Fed meet both ends of its dual mandate. However, conditions are not perfect, and the central bank likely will be loathe to raise rates until it is convinced that inflation is gaining.

As for market expectations, they center on a likely rate increase in June or September. Bank of America Merrill Lynch has been an outlier in that group, though, speculating that it's possible the Fed waits until December or later.

"We suspect the Fed is not comfortable with only a better labor market while inflation diverges further from target," BofAML economist Ethan Harris said this week in a note examining the Fed's positioning based on the chair's testimony. "Yellen's remarks reinstate the importance of the Fed's inflation objective, rather than merely assuming it will be automatically satisfied if job growth continues. And that, arguably, is an important if unspoken clarification."

Inflation, particularly through wage pressure, is likely to remain elusive, Harris argued.

Several retailers, most prominently Wal-Mart in a surprise announcement last week, have indicated they are lifting the minimum wage they will pay workers. That in turn inspired some hope that political pressure and improving economic conditions will raise pay and increase purchasing power for consumers at the lower end of the salary spectrum.

Read MoreWal-Mart wage hike may be economy's missing link

However, Harris said the sum of the efforts announced thus far—Aenta along with retailers Starbucks and Ikea also are part of the movement—will boost wage inflation only incrementally, perhaps by only 0.02 percentage point.

"The global backdrop is highly disinflationary, with weak inflation for most of our trading partners, a dramatic rise in the dollar and a dramatic plunge in commodity prices," Harris said. "All of these shocks impact U.S. inflation with a lag."

Robert Tipp, chief investment strategist at Prudential Fixed Income, said rate-hike indications from the Fed could shake what remains a fragile economic ecosystem.

"All of the objective measures that would show they need to raise rates are not giving the signal," Tipp said in an interview. "Should the Fed suggest that they're getting ready to hike rates even though those signals are not there, you're likely to get a situation like we've seen over the last year, which is a rapidly strengthening dollar."

Fed Vice Chair Stanley Fischer said Friday that he does expect a rate hike this year, but said challenges remain.

Read MoreFed's Fischer: Rate rise seen 'sometime this year'

For the rest of the central bank's policy-setters, decisions likely will remain focused on not upsetting financial markets by moving before inflation reaches the Fed target.

"By downplaying guidance changes and by shifting attention onto the inflation outlook, Yellen likely has added some volatility in the near term yet dampened excessive swings in market pricing, a la the taper tantrum," BofAML's Harris said. "That's a trade-off the Fed should be comfortable with."