Federal Reserve Chair Janet Yellen is set to appear before the Senate Banking Committee on Thursday, in the delayed second day of her monetary policy testimony. And though no major bombshells are expected, subtle nuances could speak volumes to a market hungry to learn what the Fed will do next.

Yellen testified before the House Financial Services Committee on Feb. 11, and had been slated to appear before the Senate Banking Committee on the 13th. But a snowstorm intervened, pushing the second day of her testimony two weeks into the future.

That means that Yellen, inquiring senators and market professionals alike have been granted the benefit of having seen the Federal Open Market Committee's January meeting minutes as well as some additional economic data, between the two sessions.

"The odds have gone up for something interesting to happen in day two," said Carl Riccadonna, Deutsche Bank senior U.S. economist. "This is particularly the case because we've seen the meeting minutes, and those minutes showed internal debate about what to do with the fed funds rate thresholds."

One of the Federal Reserve's key tools is the federal funds rate, which is the Fed-targeted rate at which banks lend to each other. In its January statement, the FOMC stated once again that it would keep that rate "exceptionally low ... for as long as the unemployment rate remains above 6-1/2 percent" and inflation remains low.

But now that the unemployment rate dropped to 6.6 percent in January, just a hair's breadth away from that long-watched 6.5 level, the Fed might look to change its guidance.

The problem is that the Fed is currently divided on how, exactly, to go about that.

(Read more: Kudlow: Janet Yellen's problem)

"Participants agreed that, with the unemployment rate approaching 6-1/2 percent, it would soon be appropriate for the Committee to change its forward guidance," according to the recently released minutes of the January meeting. "A range of views was expressed about the form that such forward guidance might take."

Suggestions included shifting from quantitative guidance to qualitative guidance, or including additional factors in the threshold. Other possibilities are reducing the threshold unemployment rate, or going ahead and raising the federal funds rate "relatively soon," as some hawks suggested.

"The key focus on Thursday will be any and all comments around forward guidance," Riccadonna said. "She doesn't want to commit to something, as that may upset other committee members. But she could talk about the pros and cons of different options, which would be a way of showing her hand in terms of what she favors."

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Peter Boockvar, the chief market analyst at The Lindsey Group, thinks any such hints are unlikely.

"Between her testimony and the Q&A and her hearings we saw late last year, I think everyone has a good idea of what she's thinking," Boockvar said. "The market knows the thresholds have pretty much been thrown out the window, and we know it needs to be replaced with something else, but we're going to have to sit and wait to find out what they're going to do."

BK Asset Management's managing director of FX strategy, Kathy Lien, says Yellen is "pretty much going to stick to script." But Lien added that "the bias is to the upside for the U.S. dollar," because Yellen might indicate that the Fed will continue to reduce the pace of its quantitative easing program.

"There is a lot of discussion in markets about whether the Fed is wise to continue the course of tapering, because we don't know whether there's an underlying slowdown after all this disappointing data," Lien said. "If she downplays weather distortions, and reinforces the plan to stick to tapering, it'll still lift the greenback."

(Read more: Is the US in real trouble? We're about to find out)

In terms of the fed funds rate, however, Lien is skeptical that investors will learn anything new.

"We've still got a good amount of time before the next FOMC meeting, and we've obviously got another nonfarm payrolls report between now and then," Lien said. "I think she will defer any signals on that until after the next NFP report."

Yellen's testimony is slated to begin at 10 a.m. EST on Thursday.

—By CNBC's Alex Rosenberg. Follow him on Twitter: @CNBCAlex.

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