But Boockvar does not expect to hear anything new from Dudley or two other Fed speakers Thursday. He expects the New York Fed president to repeat recent comments, including that he hopes to raise rates this year.
Tarullo told CNBC's Steve Liesman on Tuesday that based on current information on the economy, he expected it would not be appropriate to raise rates this year. His comments followed closely on similar remarks from Brainard.
"I'm not criticizing what they're saying. What they're saying, the debate is critical and it's not clear-cut. ... The question is should that debate be as public as it is, and it's unusual for the markets to deal with board members having a different view than the chair," said Diane Swonk, chief economist at Mesirow Financial.
Swonk said, however, the feeling among Fed watchers is that "people are really digging in. It's especially unusual and surprising to me given how much agreement there is to the fact that nobody wants to derail this expansion."
Not since the era of former Fed Chairman Paul Volcker have central bank members seem to have been so out of sync with the chairman, said Chris Rupkey, chief financial economist at Bank of Tokyo-Mitsubishi.
"You almost have to go back to when Volcker had his problems, in the 1980s when people were voting against him, to see the committee so split," he said. "I don't know if Brainard and Tarullo really think the economy is that iffy here that they have to delay liftoff or they're putting more votes out there to balance those that want to go," said Rupkey.
Either way, the public discord comes not long after the Fed's Sept. 18 decision to hold off raising rates for the first time in nine years because of the potential for international and financial developments to hurt the economy. Wall Street economists were close to evenly split on the chances for a September rate hike, so the Fed ended up surprising some in the markets when it chose to hold off.
Yet, Fed officials, including Dudley and Vice Chairman Stanley Fischer, the two seen as closest to Yellen, continued to say they would like to see a rate hike this year. That leaves the October meeting, which is viewed as unlikely, and the December gathering, given less than 30 percent odds by the markets.
At the same time, Chinese data have continued to be wobbly and there are signs China's weakness is spilling into the global economy. U.S. economic data are also beginning to soften. Economists now have an average third-quarter GDP forecast of 1.7 percent, according to a CNBC/Moody's Analytics survey.
Boockvar said he counted 31 Fed speeches since the September meeting, not including interviews granted by Fed officials. "This of course is the new era of transparency, but we can also call it communication overload that leaves us just as confused about the direction of monetary policy," he noted.
Besides Dudley, there are two other Fed speakers Thursday but neither is expected to have the potential for market impact. St. Louis Fed President James Bullard makes opening remarks at a conference on policy at 10:30 a.m., while Cleveland Fed President Loretta Mester speaks at 4:30 p.m. on economic growth.
On Tuesday, the Fed once more intrigued markets, when the minutes of the board's discount rate meeting revealed that eight of 12 Federal Reserve banks had requested an increase in the primary credit rate at the September meeting.
"Investors are tired of being knee jerked between Fed speakers. Last week it was hawkish presidents and this week it was dovish governors. They're just watching the data and appropriately adjusting their predictions of the Fed based on data rather than on guidance," said John Briggs, head of strategy at RBS.
He said the latest comments from Brainard and Tarullo highlight an inconsistency in the Fed's messaging. In an Oct. 1 survey, RBS found that 62 percent of nearly 100 institutional investors said the central bank's guidance has lost credibility.
"We don't know if there's a revolt but it shows there's really a debate," said Briggs.
So as the October meeting approaches, the Fed has been under more pressure to clarify its message. At the same time, the data have become murkier so it will need to rely more on current economic releases.
The markets have become used to hearing mixed messages from Fed officials, but the fact it is trying to end years of extraordinary policy makes every comment more critical. The Fed's openness was a hallmark of former Fed Chairman Ben Bernanke's tenure, and it was Yellen who spearheaded communications when she was part of Bernanke's team.
Swonk said the Fed needs to speak clearly about what it would use as rules for a rate hike when it meets in October.
"There is enormous agreement, they could pause after liftoff. But disagreement over the timing of liftoff is getting much more heated and personal than I would expect and I think it's legitimate that it should be a very rigorous debate because they are trying to decide which would be worse," said Swonk.
The data, just even in the last week has been mixed, with softer retail sales, weaker than expected producer prices, flat business inventories, but low weekly jobless claims, at the lowest level in four decades. Core CPI gained 0.2 percent in September, as expected, while PPI was weaker.
"I think the market is disillusioned by the Fed because of the confusion they've created in investors' minds. But putting that aside, what we're left with is a slowing global economy, a domestic economy that's extremely mixed and earnings that are challenged, even excluding energy," said Boockvar.