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What to expect after Yellen's statement: Analyst

The Federal Reserve is unlikely to raise interest rates in June as expected after Janet Yellen said on Tuesday that it would not hike rates for the next few Federal Open Market Committee meetings, Mesirow Financial's chief economist told CNBC.

Diana Swonk said the chair of the Fed's Board of Governors is being careful to avoid another taper tantrum, or an adverse market reaction due to unexpected comments from the central bank.

U.S. bond yields spiked in May 2013 after then Fed Chair Ben Bernanke said the central bank could wind down its monetary easing program by the end of the year.

Read More Yellen: No rate hike for next couple FOMC meetings

"This is a Fed that wants to sort of glide the path," Swonk said in a "Squawk on the Street" interview. "They're going to do this incrementally, glacially. But they do want to get liftoff this year."

The central bank could raise rates in increments of less than 25 basis points when it does take action, she said.

Yellen's prepared statement also said U.S. labor markets have room for improvement, and low oil prices will be a significant benefit to the economy. The Fed also would like to be confident that inflation will rise to 2 percent before it raises rates.

Yellen has left herself an "enormous amount of flexibility," Art Cashin, director of floor operations for UBS at the New York Stock Exchange, told "Squawk on the Street." Cashin said he thinks there is a 50-50 chance that the Fed will raise rates this year.

Read MoreLive Blog: Yellen's testimony before Congress

Even if the FOMC were to remove the much watched word "patience" from its statement at its March meeting, it would likely be at least two more meetings before the committee announces a rate hike, he said.

"March is an ideal one because it has a press conference after it, so whatever they do, she can get up and explain it after that," he said.

Yellen will likely get a "bit of a break" while testifying before the Senate banking committee on Tuesday after Sen.Elizabeth Warren, D-Mass., and other Democrats on the committee said they would not support an audit of the Fed.

"That's a bit of a turnaround and a bit of a vote of confidence for Janet Yellen at a time when the partisan politics have been very bad and it had been bipartisan attacks on the Fed," Swonk said.

Sen. Rand Paul, R-Ky., has been leading the charge in the "Audit the Fed" movement.

Read More'Audit the Fed' bill would bend monetary policy: Fisher

The central bank's financial statements are already audited each year by an independent firm, and the Government Accountability Office reviews a number of the Fed's activities.

Instead, the movement "would subject the Federal Reserve's conduct of monetary policy to unlimited congressional policy audits," Fed Gov. Jerome H. Powell said in a recent speech.

Powell warned that would essentially empower Congress to interfere with long-term monetary policy, which could have adverse effects because elected officials make decisions based at least in part on short-term political maneuvering.

Yellen faces a tougher crowd when she goes before the House of Representatives on Wednesday, where the issue of Congress' rights and control over the central bank will likely come up, Swonk said.