NEW YORK ( TheStreet) - The battle over the Obama administration's pick to be the next Federal Reserve chairman -- whether it is Larry Summers, Janet Yellen or someone else -- raises overlooked questions about a key position directly below the central bank chief- that of the Fed's top bank supervisor. Since 2009, that role has been filled by Daniel Tarullo, a member of the Fed's board of governors, in a semi-formal basis. Fed Chairman Ben Bernanke, who most observers agree will step down by the end of the year, has largely given Tarullo free rein to carry out his own ambitious regulatory agenda for big banks, including tough capital and leverage restrictions that could eventually drive some large financial institutions to downsize and divest assets or raise billions of dollars in capital. All of this has made Tarullo persona non-grata with the bank lobby. "The banks are unhappy with Tarullo because he is trying to make changes to how they do business," said a former top bank regulator. The former Georgetown University law professor has often succeeded at getting reluctant Fed governors to back his efforts and he has unveiled a to-do list of harsh restrictions to come, including a measure that would set forth just how much long-term debt and equity a megabank must maintain so that its collapse doesn't cause collateral damage to the markets. Tarullo's effort in this regard is particularly notable because Sunday marks the five-year anniversary of the failure of Lehman Brothers Holdings Inc., the first in a series of big bank collapses that wreaked havoc on our economy. The delay in implementing these changes, which are enshrined in the post-crisis Dodd-Frank Act approved three-years ago, demonstrates the difficulty Tarullo and other bank regulators have faced implementing banking rules since the crisis abated. As the Obama administration looks to replace Bernanke at the top of the central bank, it is unclear whether Tarullo will remain in control of the Fed's bank capital and rule-setting agenda. Some observers contend that Tarullo -- already at the Fed for four-and-a-half years -- will resign unless he is installed formally as vice-chairman for supervision at the Federal Reserve, a position that was authorized as part of the Dodd-Frank financial reform law. A Fed spokeswoman declined to comment.