President Obama walks with his wife, Michelle, and their two daughters, Sasha and Malia, in October. (Pool/Getty Images)

Throughout his time in office, President Obama has opened many outside-the-Beltway speeches with a suggestion that he, too, feels like an outsider in the nation’s baffling, frustrating capital city. He shouts to the audience about how good it is to be wherever he is that day — Cleveland, Miami, San Francisco. Then he takes pokes at the town where great success in his chosen profession has brought him.

“It is good to be out of Washington,” he often says — a line that, in good times and in bad, always generates warm, sympathetic applause.

Changing Washington may not have come off as Obama promised. But for the president and his supporters, the city has been an object of contempt they can believe in.

Now, though, Obama has raised the possibility that he might remain a resident of the capital after his lease on 1600 Pennsylvania Ave. expires in January 2017.

In an interview this week with Barbara Walters of ABC News, Obama and the first lady, Michelle, said they may live in Washington beyond their time in the White House to allow their younger daughter, Sasha, to graduate from Sidwell Friends School.

Sasha would be a high school sophomore at the end of the president’s second term, giving the family a couple years to enjoy, or endure, Washington as private citizens.

“We gotta make sure that she’s doing well . . . until she goes off to college,” Obama told Walters, according to an advance transcript of the interview, which aired Friday night. “Sasha will have a big say in where we are.”

For a couple who celebrate the city of Chicago as often as they skewer Washington’s nasty political culture, the suggestion that they may stick around past the constitutionally mandated time is surprising. And it highlights the reality that despite the cloistered and well-supported lifestyle of the American presidency, the Obamas are in some ways working parents who face a set of decisions not unfamiliar to others their age.

Obama would be the first former president to remain in Washington post-presidency since the dying Woodrow Wilson more than nine decades ago. A former president is an easy political target, and to stay in Washington is to be a close-range one as well. The journey from leader of the free world to the person most to blame for the early problems of a new administration is as short as a walk across Lafayette Square.

Most find it best to be far from the scene of the alleged crimes when the accusations start flying. George W. Bush, who moved back to Texas and began painting, was relatively well-served by that distance when Obama pointed often to his predecessor as the cause of the economic and fiscal problems his administration faced early on.

Sticking around is “a terrible idea and I can’t imagine it will last very long,” said Stephen Hess, a presidential scholar at the Brookings Institution. “Once you’re in Washington you are somehow connected to every problem that your predecessor is going to be confronting. And you will be asked to say something each time your name comes up, given that you will have reporters camping out on your doorstep.”

This, in part, is the reason many former presidents don’t flee just Washington, but public life entirely.

Ronald Reagan and Lyndon B. Johnson vanished onto beloved ranches in California and Texas, the former to enjoy his last years in a pretty valley north of Santa Barbara and the latter to lament what might have been if not for Vietnam.

Both men were getting on in years by the time they left office. Younger occupants such as Jimmy Carter and Bill Clinton remained active on the world stage after their presidencies rather than in the tiny arena that is official Washington.

As for the Obamas, “they are still trying to figure it out,” said Josh Earnest, the White House principal deputy press secretary. “It is certainly something they have been thinking about, and that is evident in the answer they gave.”

Earnest said the decision will likely be made late in the president’s term and pivot largely on Sasha, who is 12 and in seventh grade. Malia, 15, a high school sophomore, will have left for college by then.

“I think it is school and Sasha being able to keep her social group as much as possible — that is what is most important to them,” Earnest said.

The Obamas have kept their home in Chicago’s Hyde Park neighborhood, staying there on some visits home. Their departure was always meant to be temporary. As Valerie Jarrett, a close family friend and senior adviser to Obama, said as the family decamped for Washington, “It is really not goodbye. Rather, Chicago will say, ‘See you soon.’ ”

Michelle Obama, if not her husband, has raised the prospect of picking up post-White House life somewhere other than the city where she grew up. Last year, she said on two occasions that the family may not return to Chicago, as much as she loves the city.

“While I like going back to Chicago — I like to see the lake — this is home now because this is where we’ve built our lives,” Michelle Obama told USA Today in May 2012. “And when it’s time to leave, we’ll build it somewhere else.”

The Obamas’ frequent knocks of Washington have focused on the politics — the K Street money and the 24-hour punditry, the partisanship on Capitol Hill and the culture of point-scoring, which the president and his predecessors have said comes at the expense of the country.

Obama’s message about the city: Hate the players, not the playground. But how much Obama and his family like Washington as a place is a bit of a mystery .

At the start of Obama’s presidency, the first couple dined out with some frequency, not only on special occasions such as anniversaries but also for regular date nights. The Obamas seemed to embrace the city as much as the city embraced the new administration in the afterglow of a historic election.

Those nights out have become less common, and off-hours Obama now leaves the White House most regularly for the fairway-to-green seclusion of 18 holes at Andrews Air Force Base.

So what would private life in Washington look like for an ex-president?

That is hard to say, given that the most recent precedent is Wilson, who remained in town after his presidency ended in 1921 largely because he was suffering the debilitating aftereffects of a stroke.

One unknown is what Obama, who will be 55 when he leaves office, will want to do after his presidency.

There are law schools where he could pick up his teaching career — a vocation he says has informed his presidency — and any private home the couple may choose would certainly have a place for him to hide away and write the inevitable memoir of his presidency, even if his presidential records and library would be somewhere else.

That work could take the couple through Sasha’s graduation — and then, perhaps, far from a city traditionally full of transients who find it hard to love it.

“It’s just not a very congenial place to hang out,” Hess said.