Bloomberg News

“We are not as divided as our politics suggests,” said the man who had just been re-elected president with barely 50 percent of the vote. For Barack Obama, it was the best kind of rhetoric: a self-serving statement that also happens to be true.

The president’s remarkable victory over Republican nominee Mitt Romney last night was a near-landslide in the Electoral College, especially if his lead in Florida becomes official (with almost all the results in, it stands at about 46,000 votes). And if his current share of the popular vote holds, he will be the first Democratic president since Franklin D. Roosevelt to be re-elected with a majority.

But politics is about more than numbers — and besides, the president still has to deal with a truculent House of Representatives, which got much more conservative (if only slightly more Republican) Tuesday. It is also about persuasion. In that sense, the president’s rousing yet realistic victory speech was the night’s most encouraging development.

Gone was the heavy-lidded, monotonous lecturer of last month’s first presidential debate. Absent was the sarcastic, occasionally churlish campaigner of the last several weeks. This was vintage 2004 Obama, considerate of those who may disagree with him and pledging to work with his opponents. “I also look forward to sitting down with Governor Romney to talk about where we can work together to move this country forward,” the president said, to polite applause.

Romney, for his part, was warm and graceful in defeat — where was that guy last spring and summer? — while House Speaker John Boehner offered the president congratulations and a commitment “to find common ground.” Who knows? Maybe Romney will join the Obama Cabinet as the nation’s first secretary of business, and Boehner will revisit the grand bargain to reduce the debt that he and Obama came so close to striking in the summer of 2011.

Or maybe not. Once the shine of victory and the sting of defeat wear off, Washington could easily sound a lot like it did before the election. This is not to downplay the importance of Obama’s victory; it will allow tens of millions of uninsured Americans to get health care, to cite just one benefit, and it protects a woman’s right to an abortion, to cite another. Historic challenges facing the nation’s budget and economy remain.

Bipartisanship will not by itself solve these problems, as pundits of the left and right are fond of pointing out. It is, however, a necessary condition to any solution. To favor bipartisanship is not to require that both sides agree. At this point, it would be nice if they could just communicate.

One of the virtues of Obama’s speech is the way it acknowledged both the difficulty and necessity of this negotiation. “I’m not talking about blind optimism, the kind of hope that just ignores the enormity of the tasks ahead or the roadblocks that stand in our path,” he said. “I’m not talking about the wishful idealism that allows us to just sit on the sidelines or shirk from a fight.”

Compare this forthrightness to his victory speech of four years ago, with its vague plea to resist “partisanship and pettiness and immaturity.” This is the kind of gauzy language that so enraptured Obama’s supporters and so enraged his opponents: They both suspected he was talking about the latter.

In 2008, Barack Obama was the very embodiment of change. In 2012, he led the party of the status quo. In part this is a job requirement for any incumbent seeking office. Yet it also has to do with the maddening, fatuous notion of “change” itself. Would a Romney presidency have represented “change”? Or would it have represented a return to the pre-Obama status quo? Did Obama fulfill his promise of bringing “change” to Washington? Or is his administration evidence of the impossibility of the task?

The answer, of course, is all of the above. “Change” is in the eye of the voter. At any rate, Obama — and his supporters, to judge from Tuesday’s impressive near-sweep of swing states — seem to have traded in a generalized desire for change for a grim determination to see his changes through. This is progress, for both the president’s supporters and opponents: In politics as in language, defining terms is always helpful.

For our part, we’re happy that Obama seems to have retired his cranky candidate persona. If his early-morning address was the first speech of his second term, then there is reason to be — pardon the term — hopeful about the next four years.