Read MoreDruckenmiller: Fed policy 'fraught with...risk'
"The Fed chairman always is facing pressures from labor unions, from Congress, the administration, the business community. She has to pick which way she's going to lean. So far she's leaning in the direction of easing," Meltzer added. "That's exacerbating her problems with Richard Fisher and several other members of the Open Market Committee. Several of the presidents have become quite outspoken about the need to stop the easing policy."
To be sure, Yellen is likely to continue to win the day on the FOMC. She's been clear about keeping interest rates anchored near zero even as the Fed unwinds its monthly bond-buying program known as quantitative easing.
Markets have responded in kind, with the S&P 500 chopping its way to a 6.9 percent gain in 2014 while interest rates remain low.
Although Yellen may still win monetary policy battles within the Fed, she risks losing the economic war if, as some expect, inflation already has heated up and will continue to run higher and the Fed refuses to budge on rate policy.
"Richard Fisher thinks there is real reason for concern, as do I," Meltzer said. "The Fed has a long history of being very slow to respond to emerging inflation, very reluctant to give up ease, and that seems to be Chair Yellen's position."
Read MoreBigger worry than geopolitics? The Fed, of course
Her problem, Meltzer said, is that she is too focused on employment and believes that continued slack in the labor market requires the Fed to keep short-term rates near zero.
"She is by training and experience a labor economist, never very well acquainted with financial information except as a member of the Fed," he said, later adding, "My biggest problem with Janet Yellen is she's trying to do something she can't do."
Economist David Rosenberg also is concerned with Fed policy, reasoning that the central bank is not paying enough attention to selected wage increases as the monthly nonfarm payrolls report shows wages increasing by barely 2 percent. Pointing to an article in USA Today, Rosenberg said the top 20 percent of industries in terms of pay are averaging salary increases of 3 percent.
Of the Fisher op-ed, Rosenberg said, "I could have written this piece, but likely not nearly as well."
"Where I may disagree is that wages are not the cause of inflation but a response to inflation," the Gluskin Sheff strategist wrote in his morning analysis Monday. "It is the last piece of the inflation puzzle to move in any cycle, and for the Fed to target wages is a bit foolish in my view—targeting the most lagging of all the lagging indicators instead of the pressures that lead the process."
Such thinking is helping to trigger internal strife at the Fed.
Read MoreYellen: No 'magical formula' for rate increase
In addition to Fisher, Philadelphia Fed President Charles Plosser could dissent, as could newly seated Cleveland President Loretta Mester, according to a note from U.S. economist Michael Hanson and others on his team at Bank of America Merrill Lynch. Though he's not currently a voting member, St. Louis President James Bullard said in a recent speech that rates may need to rise "sooner rather than later."
Investors, though, shouldn't worry about a policy switch.
"The hawks are a steady source of misleading remarks about the Fed's policy path," Hanson said. "Several have already suggested that rate hikes should begin soon, or at least sooner than the market is currently pricing in. We would recommend fading their comments: They have a fundamentally different take than the majority, but are too few in number to shift the debate on the FOMC."
That doesn't mean there won't be debate.
Mohamed El-Erian, the chief economic advisor at Allanz, believes the Fed is worried about five issues: How its policies are increasing market instability; whether its policies are helping reverse the effects of the last recession; whether a falling unemployment rate will push wages and inflation higher; the effects of geopolitical unrest; and whether the Fed is bearing too much of the burden to fix the struggling U.S. economy.
Read MoreLooks like the Fed wants to have even more power
"Investors should not be lulled into complacency by the Fed's outward calm." El-Erian said in a post for Bloomberg. "We are getting closer to the point where the Fed will have to make some difficult decisions, and will face greater challenges in maintaining the buoyant, placid markets to which we have become accustomed."
Despite the push from within and the challenges the Fed faces, Yellen likely will press to keep policy along the easy route.
"That's the way she leans, and it's usually hard for the Fed to overcome the chair," Meltzer said. "It's hard to think of examples where that happens. It doesn't happen very often."
—By CNBC's Jeff Cox