“Ben Bernanke turns out to have better political instincts than anybody thought,” Mr. Frank said in an interview last week. “They accept the fact that I know what I’m doing up here.”

On one front, the Fed faces populist anger from both left-wing Democrats and right-wing Republicans about its power and secrecy. At the same time, officials are locked in brutal but arcane battles about who should oversee Wall Street and big banks as Congress tries to pass a sweeping overhaul of financial regulation.

Last summer, the central bank hired an experienced Democratic hand and former lobbyist, Linda Robertson, to help deal with members of Congress. Mr. Bernanke alone has met privately with about 40 senators and many House members in the last few months, sometimes to dissect arcane policy issues and sometimes just to explain what he does in plain English.

At one recent meeting, Senator Sherrod Brown challenged Mr. Bernanke’s bona fides as a regular guy by giving him a pop quiz on baseball statistics. Mr. Bernanke, a passionate fan, passed.

Mindful that Democrats now control the White House and Congress, Mr. Bernanke put up virtually no opposition to President Obama’s proposal for a new consumer agency that would take over the Fed’s authority over consumer lending issues. Similarly, he avoided a bruising turf battle by agreeing that the Fed would share responsibility with other regulators to monitor systemic financial risk.

But Fed officials have been steely in protecting their two top priorities: the Fed’s political independence on monetary policy and the Fed’s role as undisputed overseer of financial institutions deemed “too big to fail.”

Image Representative Barney Frank, left, said of Ben S. Bernanke, the Fed chairman, right: “Ben Bernanke turns out to have better political instincts than anybody thought.” Credit... Andrew Harrer/Bloomberg News

Mr. Bernanke took over the Fed nearly four years ago with less political experience than his predecessor, Alan Greenspan. And because he was forced to bail out companies and credit markets in such visible ways, Mr. Bernanke has enjoyed little of the mystique and distance that Mr. Greenspan used to his advantage.