Now that Larry Summers has pulled his name for consideration to be the next Federal Reserve chairman, President Barack Obama's safest choice is Janet Yellen, but keeping Ben Bernanke may still be a possibility, said Tony Fratto, former White House press secretary in the George W. Bush administration.
"Whenever people would say the White House really wants Larry Summers, I would say … who's their second choice," Fratto said on "Squawk Box" Monday, "because the opposition to him was deep and personal, and at some levels very vicious."
The withdrawal Sunday of Summers—a former Bill Clinton-era Treasury Secretary and more recently a top Obama economic adviser—followed growing resistance from Democrats on the Senate Banking Committee, which is the panel charged with sending any nomination to the full Senate for a vote.
U.S. stocks futures on Monday were strongly higher on the news. (Read more: Get ready for a Summers rally in the stock market)
"The safest choice is Yellen," Fratto continued. "I think one choice nobody has really talked about, which I really believe is still a possibility until someone rules it out, is that you keep the best guy for the job in the job—that's Ben Bernanke."
"Even it Ben Bernanke, who in my view has been heroic, would have been nominated for a third term I think that would have been a bruising confirmation with a number of Republicans opposed to it," Roger Altman, deputy Treasury Secretary during the Clinton administration, told CNBC Monday. "This reflects the degree to which the Federal Reserve itself has been politicized."
Altman, who had been a supporter of Summers, said that the opposition to his nomination is "testimony to the continued fallout from 2008, and the continued deep antipathy on the part of the public towards Wall Street and the broader financial community. And that played out here in a perception ... that Larry was too close to Wall Street."
Former Massachusetts congressman Barney Frank said he agrees with Altman on that point in a separate "Squawk Box" interview Monday, along with former Connecticut senator Chris Dodd, Frank's co-author on the Wall Street reform bill that bears their names.
"Larry made the right decision given the Senate opposition," the Democrat Frank continued. "[But] if I had been a senator, I would have voted to confirm him."
Fellow Democrat Dodd said while it would have been tough, the president would have gotten Summers through the confirmation process. "It would have been ugly and would have taken a long time," he said. "[But] presidents normally get their choices in these matters."
The exit of presumed frontrunner Summers could open the door for Fed Vice Chair Yellen, who if chosen by Obama would become the first woman to lead the central bank.
(Read more: Summers withdraws his name for Fed chair)
In the past, Obama has mentioned only one other candidate as possibly being under consideration: Donald Kohn, a former Fed vice chair. But Kohn has been considered a long shot.
The administration also reached out to former Treasury Secretary Timothy Geithner early in the process. Geithner has said he's not interested in being considered and he's still said to feel that way.
Obama is expected to announce a nominee for the Fed chairman as early as this month. Bernanke's term at the helm ends Jan. 31, 2014, and all indications have been that Bernanke does not want to continue in the job for a third term.
The other big question for market concerning the Fed is when it might start to scale bank its $85-billion-a-month bond-buying program. Central bank policymakers are scheduled to meet this week and investors are hoping for answers.
—By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC.