During Bill Clinton's presidency, I once listened to a senior White House aide complain about the amount of time his boss spent meeting ordinary citizens. There was always a sob story, the aide said, and the president would return to the Oval Office demanding that his staff waste precious time addressing it.

This episode popped into my mind last week when I read about how throngs of Brazilian believers had mobbed the car carrying Pope Francis through the streets of Rio, pressing so close that the vehicle had to stop several times.

"While local and national officials traded barbs over who screwed up in Rio, Francis made the most of the mishap," a report said. "To the despair of Vatican security, he threw open his window, waved at his flock, patted hundreds of heads and kissed eight babies while worshipers and tourists trotted alongside the convoy."

But why call it a mishap? Getting close to the people is an achievement to be emulated, not a security lapse to be explained. One of the great failures of the American constitutional experiment is the growing distance between the president and his public. For all that our presidents bemoan the bubble in which they live and travel, they spend too little time thrusting themselves into crowds and meeting the people.

In his book "Prisoners of the White House: The Isolation of America's Presidents and the Crisis of Leadership," veteran journalist Kenneth Walsh writes that presidential isolation is getting worse. The isolation exalts the role of experts who encourage their client to rely on polls and focus groups to decide what the people think.

Our chief executives are too often surrounded by a "cadre of idolizers," he writes, who insulate them from criticism and questions. For all the talk in recent decades of the imperial presidency, nothing is more monarchical than the increasing physical separation between the man who holds the office and the people on whose behalf he serves.

An obvious solution is for our presidents to follow the example of Pope Francis and actually meet their public — not at staged events with carefully vetted crowds asking carefully vetted questions but at times and moments when anybody can have a chance.

Perhaps we should revive a great American tradition that was practiced, unbroken, from the time of George Washington through the administration of Herbert Hoover:

Once a year, on Jan. 1, the president would make himself available to shake hands with as many people as waited in line.

The levee, as it was often called, took place at the White House. The most ordinary of men and women could put on their best clothes and file through what is now the Blue Room, shake the hand of the chief executive and even exchange a word or two.

For a time, the tradition was so important that the diplomatic corps was invited. Leading members of Congress and of the Cabinet — back when the Cabinet was far more powerful than it is today — were also in attendance.

The levee could serve an important instructional function as well. Consider the following report from the New York Times of Jan. 2, 1864: "Years ago had any colored man presented himself at the White House, at the President's levee, seeking an introduction to the Chief Magistrate of the nation, he would, in all probability, have been roughly handled for his impudence. Yesterday four colored men, of genteel exterior and with the manners of gentlemen, joined in the throng that crowded the Executive mansion, and were presented to the President of the United States."

The message to the nation could hardly be missed.

Why did the tradition end? Because Hoover, irritated and exhausted after shaking thousands of hands on Jan. 1, 1932, turned to his wife and said, "Next year, we'll spend New Year's in Florida." His successor, Franklin Roosevelt, not wanting to be seen in his wheelchair, was hardly the man to resume it. After that, there was World War II, followed by the Cold War, followed by the war on terror, and … well, once the decision is made to wall the president off from the people, one can always invent a reason.

Walsh, analyzing the presidencies from FDR's on, gives high marks to Clinton and Ronald Reagan, cheerful men whose outgoing personalities set a tone that allowed them more frequent escapes from the bubble. Richard Nixon and Jimmy Carter barely even tried. For Barack Obama, writes Walsh, the struggle to stay close to the public has been made difficult in part by a staff that shunts aside advisers who "shake him up too much."

Certainly the president is busy, and there will be security concerns to be resolved, but moving the presidency closer to the people is in the national interest. "I call these receptions my public-opinion baths," Lincoln once said. He added: "Though they may not be pleasant in all their particulars, the effect as a whole is renovating and invigorating to my perceptions of responsibility and duty."

As it happens, Jan. 1, 2014, will mark the 150th anniversary of that day when Lincoln showed that the White House was truly open to all comers. If the Obama administration starts planning now, it has plenty of time.

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Stephen L. Carter is a Bloomberg View columnist and a professor of law at Yale University.