The Fed's purchases have swollen its investment portfolio to $3.7 trillion, a record by far. Eventually, perhaps under Yellen, the Fed will have to start unloading the bonds without shaking financial markets. It will be a tough task.
Yellen would also take over the Fed at a critical time for China, the world's No. 2 economy after the United States, and other developing nations.
The International Monetary Fund, citing slower growth in China, India and Brazil, downgraded its forecast this week for global economic growth to 2.9 percent this year and 3.6 percent in 2014. Both are 0.2 percentage point weaker than the IMF's previous forecast in July.
Investors have been pulling money out of developing markets, partly to take advantage of rising interest rates in the United States. The Fed might be called upon to help calm worldwide financial volatility.
“The role of the Fed chair is so critical,'' said Greg McBride, senior financial analyst at Bankrate.com. ``We're not just talking about the U.S. economy. We're talking about the global economy.''
Yellen will also have to establish herself as chair at a time when the Fed is experiencing unusual turnover. When Bernanke leaves Jan. 31, but there could be up to four vacancies that Obama would need to fill on the seven-member Fed board.
One board member, Elizabeth Duke, left in August. Another, Sarah Bloom Raskin, has been nominated by Obama to become deputy Treasury secretary. The term of a third, Jerome Powell, will be up Jan. 31, though he can remain on the board until a successor is confirmed by the Senate.
And Sandra Pianalto, president of the Federal Reserve Bank of Cleveland, has announced that she will leave early next year.
Most analysts say they're confident Yellen can handle the many challenges.
“By temperament, by mannerism and by extensive experience, I think she is better prepared for that job than almost anybody on the face of the earth,'' says Alan Blinder, a Princeton University economist and former Fed vice chairman who served with Yellen at the Fed in the 1990s.