U.S. President Barack Obama has won a second term in the White House. His victory was narrow, but it was definitive. Equally important for him, his Democratic Party retained control of the U.S. Senate. On the other hand, as expected, the Republican Party maintained its majority in the House of Representatives.

The results mean that divided government continues in Washington. Mr. Obama has been vindicated, but the president faces the same problem he encountered in the last two years: a Republican Party that believes in no-holds-barred opposition.

It was a convincing victory for Mr. Obama, who prevailed in both the popular vote and the electoral count. There was some concern that he would win the latter while Republican candidate Mr. Mitt Romney would take the popular count, which, while not unprecedented, would have fed a Republican Party narrative that the president lacked a mandate and that his second term was flawed or somehow illegitimate.

The Democratic Party not only retained control of Senate, but actually picked up seats, giving Mr. Obama more leverage in his dealings with the opposition. Looking at the turnout and the vote, Mr. Obama and fellow Democrats have many reasons to be happy, and not just by the outcome. They proved that they have a formidable ground game that is capable of finding and motivating voters even in a weak economy. They garnered strong support from important constituencies, in particular, women, youth and Latino voters, the country’s fastest growing ethnic group. While Asian Americans are not so large or visible a constituency, Mr. Obama swept them as well.

If there is a cloud on Mr. Obama’s horizon, it is the continuing Republican grip on the House of Representatives. There was very little realistic chance that the Democrats would claim a majority; the sheer number of seats that would have to be “in play” and the way that districts were redrawn in 2010 (the usual outcome of a national census) practically ensured continued GOP dominance of the chamber.

The key question now is how the House — and the Republican Party — will respond to the president’s re-election. The Republican Party remains deeply divided between its conservative base — dominated by, but not the same as, the tea party — and a more traditional wing, personified by former President George H.W. Bush and former Secretary of State Colin Powell.

The conservatives are, to be blunt, ideologues who believe in the pursuit of principle; for them, compromise is a dirty word. The second group believes in many of the same principles — small government and lower taxes top their list of priorities — but they are prepared to shave off the sharp edges of their platform to get results. In short, they are moderates who are prepared to meet the Democrats halfway.

Thus far, the ideologues have prevailed. There were hopes that the Republican Party would take control of the Senate, but the base put up candidates in several races who alienated moderate and independent voters — as well as made extraordinary gaffes during the campaign — that ensured Democratic victories.

Mr. Romney tacked hard right in the campaign to win the nomination and then back to the center once he was the nominee in an attempt to win over the center, but that effort fell flat.

The key question now is whether the Republican Party will conclude that the problem was that Mr. Romney was not conservative enough or that the party should moderate its hardline positions. Some observers predict a bloodletting in the party as it struggles to reconcile the two positions. The outcome matters for the United States and the world.

A Republican Party that lurches further to the right will fight Mr. Obama on every item and try to paralyze government. A deadlock will prevent agreements on a budget as well as raising the debt ceiling. Gridlock in Washington will trigger massive cuts in the budget, including defense. This outcome could undermine the U.S. position in Asia and U.S. credibility more generally.

While in some ways, the outcome is out of Mr. Obama’s hands, there is much he can do to try to avoid this disaster. First, he must reach out to the GOP and make real his promise to be the president of all Americans. Republicans must be given the chance to be part of the government — not only in the Cabinet, where there is traditionally a member of the opposition — but also within Congress. Republicans need to feel that their views are heard and respected. Of course, the Republican Party must be sincere about compromise as well. Demanding, as some in the party do, that the president adopt their positions as a condition of their support is not compromise.

President Obama must also be more forthright about his vision and priorities for a second term. His campaign was more focused on tarring Mr. Romney than in explaining what the president would do with a second term besides protecting his accomplishments. That is not enough. Mr. Obama must lay out a plan with defined objectives for his country such as:

How will he speed up and protect the nascent economic recovery?

How will he deal with a rising and more assertive China that seems intent on intimidating its neighbors and marginalizing the United States in the region?

How will the U.S. deal with the ongoing conflict in Syria as well as Iran’s determination to push its nuclear program?

America and the world await details of his second term. Mr. Obama has been a good president in the eyes of many Americans; now he has the chance to be a great one.

Japan must continue to work with the Obama administration to maintain regional stability, while at the same time upholding the Constitution’s no-war principle.

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