She avoided making any big monetary policy news in two appearances on Capitol Hill this week, but Federal Reserve Chairwoman Janet Yellen couldn't escape a few confrontations that raise doubts about the details of the Federal Reserve's plans to avoid bailouts in future financial crises.

On Tuesday, Yellen avoided directly answering Sen. Elizabeth Warren's question about whether the Fed is committed to enforcing a provision of the Dodd-Frank financial reform law intended to force big banks to prove they could fail without causing a panic or receiving bailouts. The law requires big banks to provide regulators plans, called living wills, for their own orderly resolution in the case of a failure.

In a hearing in the House on Wednesday, Rep. Patrick McHenry, R-N.C., followed up on Warren's line of questioning and forced Yellen to acknowledge that even though the Fed has accepted some banks' living wills, that “does not necessarily mean they are credible.” In other words, the living will provision does not guarantee that the big banks can safely be resolved without bailouts.

Yellen said Wednesday the law does not require the Fed to say whether the banks' plans are credible, but instead the Fed “can make a determination at some point that the living will is not credible” at its own discretion. The day before, Warren had maintained that the Fed is required to either determine that the living wills are credible or take measures against the banks, including breaking them up in an extreme case.

The Fed interpreted the law to allow it to accept a living will without saying whether it was adequate to prevent a bailout in its final rule in 2011, according to the law firm DavisPolk, before Yellen became chairwoman.

The second incident also came Wednesday, in an exchange with Rep. Scott Garrett, a New Jersey Republican and one of Dodd-Frank's toughest critics in Congress.

Garrett challenged Yellen over the Fed's bailout lending powers, which Dodd-Frank was supposed to curb after the Fed's large-scale bailouts for banks and nonbanks such as insurer AIG during the financial crisis in 2008.

The law's authors sought to limit Fed's power to offer bailouts -- known as 13(3) authority, after the section of the Federal Reserve Act that granted it the authority -- by allowing such lending programs only if they served all comers and not if they were intended to help a single company or group of companies.

Garrett pressed Yellen on the question Wednesday, asking her whether the Fed would bail out broker-dealers, a specific group of non-bank financial firms, with its 13(3) powers.

Yellen responded that “a broad-based scheme in the situation of systemic risk is a possibility, but it is something that would have to be very seriously considered.”

“That's quite astounding that broker-dealers and other nonbanks … are on notice” for a bailout, Garrett responded.

Yellen tried to qualify that the circumstances would have to be “unusual and exigent” before being cut off by Garrett.

Although Garrett’s aggressive questioning made it difficult for Yellen to clarify her comments, her testimony only increased the existing ambiguity over the Fed’s interpretation of the limits of its 13(3) powers.

Under Dodd-Frank, the Fed was also supposed to write rules limiting the terms for such bailouts.

When the Fed proposed the rule in January, however, critics such as Americans for Financial Reform's Marcus Stanley complained that the rule simply copied the language of the statute without adding detail, minimizing the limits on bailouts.

“There is no discussion in the proposal of what ‘broad' would mean beyond ruling out an individual institution, and whether it would rule out [bailout programs] that were heavily weighted to supporting a narrow group of institutions. This is critical because every significant financial crisis in U.S. history has involved multiple institutions, and there is every reason to believe the next one will as well,” Stanley wrote in a comment on the rule.