Three candidates for the Federal Reserve Board of Governors gained approval from the Senate Banking Committee on Tuesday morning, moving toward a full Senate vote and advancing toward confirmation to an understaffed Fed.

Stanley Fischer, President Obama's nominee for Fed vice chairman who previously served as the head of Israel's central bank, advanced by voice vote, as did Lael Brainard and Jerome Powell. Brainard is a former official in Obama's Treasury Department, and Powell, a Republican, is seeking re-confirmation after serving at the Fed for the past two years.

Sen. David Vitter, R-La., asked to be recorded as a "nay" vote on the candidates, saying the Fed is “not adequately diverse in terms of background,” noting that the board includes academics but nobody who has worked in community banking.

Elizabeth Warren, D-Mass., the freshman senator known as a critic of the U.S. banking system and its regulation, voted to confirm Fischer, but said in a statement that she did so "reluctantly" because of her "growing frustration over the concentration of people with ties to the mega-bank Citigroup in senior government positions." Fischer worked as a vice chairman at Citigroup in the early 2000s before becoming Israel's top central banker.

The confirmation process can't move quickly enough for Fed Chairwoman Janet Yellen, who faces staffing problems in the near future. Currently, the Fed's seven-member board is down to just four members, including Powell, whose term technically expired in January.

One of those four, Jeremy Stein, has announced that he will step down May 28, leaving another vacancy. At that point, the only other remaining members would be Daniel Tarullo and Yellen.

If the three candidates approved by the Banking Committee on Tuesday are not installed before then, which appears likely, the Board of Governors faces logistical headaches in carrying out its business.

The banking panel also cleared three other nominations for administration positions: Nani Coloretti for deputy secretary of the Department of Housing and Urban Development, Gustavo Velasquez Aguilar for assistant secretary of HUD; and J. Mark McWatters for the National Credit Union Administration Board.

The panel also was supposed to mark up a bipartisan bill to wind down the bailed-out mortgage businesses Fannie Mae and Freddie Mac and reform the housing finance system. Voting on the measure was delayed, however, with committee Chairman Tim Johnson, D-S.D., saying that members asked for “a brief delay to try to work out additional issues prior to a final vote.”

Both Johnson and his Republican counterpart, Sen. Mike Crapo of Idaho, said that the committee had the votes to pass the bill, which is the product of months of hearings and deliberations and builds on an early bipartisan measure introduced by Sens. Bob Corker, R-Tenn., and Mark Warner, D-Va.

In recent days, members of the committee have introduced significant proposed changes to some of the provisions of the bill, which would replace Fannie and Freddie with a system of private insurance for mortgage-backed securities backed by a Federal Mortgage Insurance Corporation. In particular, Sens. Sherrod Brown, D-Ohio, and Vitter offered amendments intended to prevent the new system from creating the risk of bank bailouts.

Crapo said housing finance reform is the “most important piece of unfinished business” left in addressing the fallout of the financial crisis, and said that he was looking forward to passing it with stronger support when it is brought up before the 22-member committee."