Bank of America (BAC) Chief Executive Brian Moynihan may be solidifying his power by firing top executives and streamlining operations, but he still has some skeptics on his board of directors--several of whom continue to question his ability to lead the big bank out of its current financial problems, sources tell the FOX Business Network.

Moynihans detractors are still outnumbered by board members who want him to stay, according to senior Wall Street executives with direct knowledge of the board members' opinions. Moynihan's strongest support comes from those board members who have close ties with Fleet Financial, which was purchased by Bank of America in 2005. His supporters are led by long-time board member Charles Gifford, a former senior executive at Fleet.

But the lack of confidence from a faction of the board--albeit still a minority--presents a major obstacle to Moynihan and his ability to remain in the post even with his management shakeup earlier in the week. Unanimous board support is usually crucial for a CEOs long-term job security, and though Moynihans job is safe for the moment, hes still under significant pressure to deal with mounting financial pressures facing the bank.

There are people on the board who think hes just not the right person for the job, said one senior Wall Street executive with direct knowledge of the matter. His biggest support comes from the old Fleet guys, but he has skeptics as well who think he should go.

A spokesman for BofA declined to comment.

As FOX Business was first to report, Moynihan launched a major management overhaul on Tuesday. In the move, Brokerage Chief Sallie Krawcheck, and Retail Bank Chief Joe Price were ousted, while Global Banking and Markets Chief Tom Montag was promoted to co-chief operating officer.

Bank officials said publicly that the moves were designed to streamline operations, making it easier for Moynihan to manage the banks sprawling operations. With $2 trillion in assets and $1 trillion in customer deposits, Bank of America is the countrys largest bank combining investment banking, brokerage and commercial banking activities.

But people with direct knowledge of the move say Moynihan was facing growing skepticism from several members of the banks board of directors about his leadership abilities. These members were described as directors who have little, if any, ties to Gifford, who is considered the banks most powerful director and was instrumental in placing Moynihan in the top job in 2009.

One issue involved dysfunction in the management ranks that some board members claim made it difficult for Moynihan to act swiftly with dealing with some of the big problems that plague BofA, such as tens of billions of dollars in potential liability stemming from the banks purchase of Countrywide Financial.

It was Moynihans predecessor, Ken Lewis, who made the ill-fated purchase of Countrywide in early 2008, but some board members continue to feel Moynihan moved to slow in dealing with the problem of potential huge losses. Not until BoAs stock began a nose dive toward $5 a share did Moynihan begin to raise capital by selling assets and reaching out to Warren Buffett for a $5 billion cash infusion.

The asset sales only temporarily relieved pressure on the banks stock, as did Tuesdays announcement of the management changes. On Thursday, shares of BofA fell 3.74% to $7.22.

As a result, Moynihan still hasnt convinced his skeptics on the board that he is the right person for the job, senior Wall Street executives say. Many Wall Street analysts believe that Montag--a long time executives at Goldman Sachs who successfully led BofAs markets unit-- is now next in line to replace Moynihan should he fail to deliver.

Charles Gasparino joined FOX Business Network (FBN) in February 2010 as Senior Correspondent.