John D. Podesta, who co-chaired of the transition team of President-elect Obama in 2008 and once served as President Bill Clinton’s chief of staff, will return to the White House as an adviser in January. (Charles Dharapak/ASSOCIATED PRESS)

President Obama is embarking on his biggest organizational overhaul of the White House since 2010, bringing in Washington veterans and rethinking the way he approaches some of the most pressing policy decisions he will make during the remainder of his second term.

The decision to enlist influential Democratic strategist John D. Podesta, just days after bringing back his former legislative affairs chief Phil Schiliro, signals a larger shift in how the White House will operate in coming months. Eager to salvage his landmark health-care law and advance climate-change policy before he leaves office, Obama and his aides are open to empowering a handful of advisers with broader policy portfolios to ensure the administration achieves its goals.

The president and his aides have been discussing a possible reorganization with some trusted outside advisers for at least a month, according to a senior White House official, who spoke on the condition of anonymity because of the topic’s sensitive nature. The staff ­changes will continue in the coming weeks, the official said.

The moves mark a recognition by the White House that it needed to change its operations in light of the botched Oct. 1 rollout of the health-care law, particularly given that Pete Rouse, the president’s longest-serving aide, will be leaving by the end of the year.

Obama has been hesitant to replace many within his small inner circle operating in the West Wing, in part because his limited time in Washington before the presidency left him with relatively few trusted advisers. While he replaced several key members of his Cabinet after his 2012 re­election — including his secretaries of state, Treasury and defense — it is a measure of how static White House staff has been that the recruitment of two former advisers, on a temporary basis, amounts to a staff shake-up.

“Obama still has an opportunity to get one or two major initiatives through Congress, possibly immigration reform, but he doesn’t have much gas left in the tank,” New York University public affairs professor Paul C. Light wrote in an e-mail. “Podesta and Schiliro may be able to ration Obama’s declining political capital, and hold the line on House Republican attacks. The door is closing on Obama’s presidency — these two advisers know how to do it as well as it can be done.”

The White House’s handling of the health-care law’s implementation, Obama’s lack of knowledge about the scope of the National Security Agency’s eavesdropping program and other missteps have damaged the president’s credibility and raised questions about the West Wing’s competence. Republican critics and Democratic allies have called on Obama to fire at least one senior staff member, a step Obama has so far resisted.

Podesta has done multiple stints on Capitol Hill and served twice in the Clinton White House, taking over as chief of staff in 1998 and steering the ship through Clinton’s House impeachment. After Clinton left office, Podesta founded the Center for American Progress (CAP), a liberal think tank, and managed Obama’s transition team in 2008.

Obama officials emphasized that the two recent hires were distinct: Schiliro will serve only for a few months and is focused exclusively on steering the administration’s health-care policy. But the moves, along with Rouse’s imminent departure, mark one of the most significant shifts in White House staffing since the ­changes Obama made in the wake of Democratic losses in the 2010 midterms.

After that election, senior aides David Axelrod, Jim Messina and Mona Sutphen left and the political director’s job occupied by Patrick Gaspard was eliminated. Obama political strategist David Plouffe came on as a senior adviser, and William Daley took over as chief of staff.

Former White House deputy senior adviser Stephanie Cutter, now a partner at the consulting firm Precision Strategies, wrote in an e-mail that adding the two advisers “brings some fresh thinking and brain power, because they haven’t been in the foxhole these last several months or even years.”

“They also bring institutional knowledge of the workings of the West Wing” and other parts of Washington, she added.

Several former administration officials and Obama supporters said the realignment amounts to an acknowledgment that the current policy and legislative affairs operations have key vulnerabilities.

The president felt the need to quiet “the chattering classes” who have suggested his team needs “more inside Washington experience,” the senior White House aide said.

One former White House official, who asked for anonymity in order to speak frankly, said the ­changes reflect a recognition that the White House’s insular leadership was no longer capable of managing the administration’s myriad problems.

Much of the key decision making rests with White House Chief of Staff Denis McDonough, Rouse and senior adviser Valerie Jarrett. Several White House officials said recruiting Podesta was McDonough’s idea. Schiliro will be focused on bolstering the administration’s relationship with lawmakers who are nervous about the health-care law’s impact and head off any further problems with the law’s implementation. The decision to bring in Podesta reflects the president’s intent to exercise his executive authority on several key fronts.

White House communications director Jennifer Palmieri said Podesta will help the administration strategize about “how do you leverage all the resources you have in the federal government to advance your agenda in a political year.”

In an interview with The Washington Post this fall, Podesta said Obama’s “path to success is going to come through every single place that you can squeeze some authority which he has. That is where you’ve got to focus your attention and where you could spend your political capital.”

Podesta will advise McDonough on climate, energy, the environment and other issues. He will start in January and stay a year, allowing him to depart in time to help former secretary of state Hillary Rodham Clinton if she launches a 2016 presidential bid.

Podesta has devoted much of his career to championing environmental issues, and he has intensified his focus on climate change since founding CAP a decade ago. He had privately urged Obama, McDonough and other aides for more than a year to appoint a senior staffer to oversee the administration’s climate efforts; now he finds himself in that post.

Podesta’s appointment was praised Tuesday by environmentalists, including leaders of the Sierra Club, League of Conservation Voters, the Environmental Defense Fund and billionaire Tom Steyer, a major Obama and CAP donor who has helped finance the opposition to the Keystone XL pipeline.

Stephen H. Brown, vice president and counsel for Tesoro Corp., wrote in an e-mail that he and other energy industry officials are worried about Podesta’s move to the West Wing.

“The ‘climate creep’ agenda of this administration — the agenda of implementing climate change initiatives via regulation and executive order that which cannot be successfully legislated — continues unabated and with an eye toward a calendar that, thankfully, runs out in January 2017,” Brown wrote.

Scott Wilson contributed to this report.