Now that President Obama has finally settled on Janet Yellen as Federal Reserve chairman, the debate has started over what happens to Gov. Dan Tarullo.

It's unclear whether he will continue to act as the de facto vice chairman in charge of supervision or if Yellen might seek to curb his power to reclaim some authority over bank policy.

But the easy bet is more of the same. As one source put it, "Tarullo is probably safe and sound for the foreseeable future."

This camp argues Yellen will be just as obsessed with monetary policy as Ben Bernanke has been and will be happy to have someone else riding herd on regulation.

But insiders are less convinced. Effective supervision of the largest banks is so central to the Fed's mission that these sources expect Yellen to get more involved. They also argue she will want to fix morale problems among the bank supervision staff uncovered by an employee survey last spring and attributed, at least in part, to Tarullo's dictatorial style

Surprisingly, it may not matter which side is right.

(To see more posts from Barb Rehm's Blog, click here.)

The Fed is in the homestretch of implementing Dodd-Frank, so much of the work that remains may be in place by the time Yellen takes over the central bank on Feb. 1. What's more, there doesn't appear to be much daylight between Yellen and Tarullo on key bank policy issues. They both support higher, stronger capital requirements, including surcharges for the biggest banks. They both support tougher macroprudential standards, stress tests, capital plans, living wills and orderly resolution.

Yellen and Tarullo are also in sync on further actions that need to be taken. They both endorse a tough long-term liquidity standard, limits on short-term wholesale funding and more oversight of money market mutual funds.

So there are better questions to ask then whether Yellen will rein in Tarullo.

Those include: Will the White House nominate a vice chairman for supervision? If it does, will it choose Tarullo?

When sources first raised this, I dismissed it because if the White House hasn't nominated anyone for that job in three-plus years, why would it now? Leaving that job vacant is one of the many mysteries of the Obama administration's confounding nominations process.

But there's a new piece to this puzzle, and it may force the administration to finally pick a vice chairman for supervision.

When Yellen becomes chairman of the Fed, her current job as vice chairman will be vacant.

The administration will need to fill that vice chairmanship. It is rarely left vacant and coveted by plenty of people the Obama administration wants to reward. But the Senate Republicans could insist the administration package the two vice chairmen nominations.

In other words, if the administration wants to fill the original vice chairman slot it will need to fill the one for supervision, too.

No one I spoke with thinks Tarullo will get the nod. That may be wishful thinking, but Tarullo has never made "getting along" with folks a priority and he's not popular among Senate Republicans. 

Three separate sources named FDIC Vice Chairman Tom Hoenig as a possible Obama pick for Fed vice chairman of supervision. I get that on some levels but if the GOP is going to make a political deal, I figure the industry's opinion will be taken into account. Most bankers, at least the ones at the large banks making mega contributions, would not consider Hoenig an improvement over Tarullo. These bankers are looking for someone they consider more "reasonable" like Gov. Jay Powell.

If there is a deal to get a package of Fed vice chairmen through the Senate and Tarullo isn't named to the supervision slot, most sources expect he would leave the Fed.

Ironically that would be bad for Yellen. She needs bodies on the Fed board.

At full strength, the Fed has seven board members. Once Yellen is confirmed as chairman (and I am assuming she will be), the board will be down to five members. One of those, Sarah Bloom Raskin, has been nominated as deputy Treasury secretary, and the term of another, Powell, expires on Jan. 31. He could continue to serve past that deadline and may get renominated.

But even with Powell, Yellen faces the prospect of presiding over a Federal Open Market Committee that has more members from the Fed district banks than the Fed board.

The Fed would have four members: Yellen, Tarullo, Powell and Jeremy Stein while the district banks would have five. That could make exerting her will on monetary policy more difficult. (I wrote about this in mid-August.)

So while it may be more fun to wonder how Yellen will treat Tarullo, she's probably more focused on convincing the White House to quickly fill the current and coming vacancies.