By then, the Fed will have plenty more data to review, including February jobs, but that report could be hit by weather as well.

She also made it clear the Fed would continue on a course to taper back its $65 billion-a-month bond-buying program, unless there was a notable change in the economy, so traders expect another cut of $10 billion when the Fed meets in March.

Yellen testifies before the Senate Banking Committee on Thursday at 10 a.m. EST, in her second economic testimony before Congress this month. Her first was before the House Finance Committee on Feb. 11, and she said at the time that it's unclear why the employment reports were so weak, but weather could certainly be a factor.

"I'm sure she's going to be asked about that because in between her testimonies, we've only gotten more and more weather-depressed data, so it's become more of an issue," said Tom Simons, money market economist at Jefferies.

Even on Wednesday, mixed data showed the potential for more than just weather impact, with mortgage applications at a 20-year low, but new home sales better than expected.

Yellen is expected to stick to the same opening remarks she made before the House, but the questioning is certain to be different. There could also be more focus on banking regulation and "too big to fail" institutions. Senate Banking is chaired by Tim Johnson, D-S.D., and its members include Sens. Bob Corker, R-Tenn., and Elizabeth Warren, D-Mass.

But it's unlikely Yellen will leap to any conclusions about the weather impact.

Diane Swonk, chief economist at Mesirow Financial, said housing is one part of the economy that could come up in the question and answer session. It's also one area that the Fed has been credited with helping with its programs to keep interest rates low.

Swonk said she's personally concerned the batch of bad housing data are signaling a more structural problem than just weather effect.

Yellen, however, is unlikely to be definitive. "I think right now the Fed is playing it close to the vest. There's some movement away from 'it's just the weather alone' right now, but it's in her interest to just play it close to the vest and not be too different than two weeks ago," Swonk said.



"She will have to address the transitory nature of what we're seeing. I can't imagine she is going to try to move markets. Right now, they've got to stick to the story. They have a press conference in March. They have the ability to change the forecast, an ability to change their communications," Swonk said.

The Fed has said it will consider altering short-term rates when unemployment reaches 6.5 percent. It was at 6.6 percent in January, and the Fed also has a problem in that it communicated a specific rate that might soon be overtaken.

Fed officials have said that level is a target, not a trigger for action, but it remains a point of interest by the markets.

Swonk said there is talk the Fed could drop the idea of using a specific numerical target and move to "nuance."

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

Simons also says Yellen will veer away from providing much more insight into what she thinks may be going on in the economy.

"I think part of that is that opinion is central to forming expectations for policy at this point. She is so careful about communications. She understands the weight the Fed chairman's words have all the time. She wouldn't want to do something that would unilaterally say something about policy," Simons said.

"She knows the signal to the market is much more important coming from her mouth. I expect if she's asked about the weather, she'll say something to the effect of 'We don't know, but our forecasts suggest things are going to get better.' "