Some fresh light could soon be shed on the market's biggest mystery.

On Tuesday and Wednesday, Federal Reserve chair Janet Yellen is set to testify before the U.S. Senate and House, respectively. Investors will likely be listening with keen ears, hoping for a hint about when the Fed will finally hike interest rates from their crisis-era lows.

In the minutes from their January meeting released on Wednesday, Fed policymakers appeared a bit less eager to hike rates than investors had anticipated.

In somewhat opaque language, the central bank's policy committee said that "many participants indicated that their assessment of the balance of risks associated with the timing of the beginning of policy normalization had inclined them toward keeping the federal funds rate at its effective lower bound for a longer time."

The perceived dovishness calmed fears of a June rate hike, leading short-term yields to fall sharply on the week. Currently, federal funds futures contracts are pricing in just a 15 percent chance of a rate hike by June, according to CME Group's Fed Watch tool.

However, that meeting occurred nearly a month ago, which before the release of January employment report that bested expectations. In a separate but related note, Wal-Mart announced that it was increasing its minimum pay to $9 an hour by April, and $10 by February 2016.

That may indicate that the growing labor market is finally creating a bit of wage inflation, a sorely missing part of the recovery equation that could reduce concerns that inflation will drop on the back of a rate hike.

On the other hand, recent economic data points like the Empire State Manufacturing and the Philadelphia Fed surveys have disappointed, indicating that growth could be moderating a bit. Meanwhile, worries about the global economic situation have not gone away.

It is into the midst of this maelstrom of mixed signals, market volatility and ever-adjusting expectations that the Fed chair will step this week.

"I don't envy her at all. She's in completely uncharted territory right now," said Karissa McDonough, director of fixed income strategy for People's United Bank Wealth Management.

"It seems to me that she's going to be extraordinarily careful with her wording," McDonough said, noting the Fed's nervous discussion over the risks of dropping the word "patient" from its January statement. Some policymakers fretted that if the word was dropped, "financial markets would overreact, resulting in undesirably tight financial conditions," the meeting minutes report.

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But for Michael Cloherty, head of U.S. rates strategy with RBC Capital Markets, the Fed's bigger fear now is not upsetting the market by implying that a rate hike is on deck. To the contrary, he believes that the Fed is now looking to hike in June (despite their qualifier of being "data dependent") and doesn't want the move to be too much of a shock.

"I think we'll hear more of a push toward June tightening," he said. "The Fed will really want to prep the market for the first rate hike. And the window for that sort of signal is closing. The March meeting is a little close, and the April meeting is probably too late."

"In fact, if we don't get hawkish language, we may have to slide back our expectations to the third quarter," Cloherty added. "But we think that they're going to go in June," which means Yellen is likely to send some sort of warning to the market this week.

Despite market sentiments, the strategist insists that in order to facilitate a gradual hiking of rates back, the Fed is eager to get started with its first small hike.

That would allow the Fed to avoid getting caught flat-footed if inflation does rear its head, but also to methodically observe the consequences of rate hikes in this brave new central banking world.

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