During the midterm elections, candidates largely ignored foreign policy. Not even the wars in Afghanistan and Iraq stirred much interest. In a period of economic unease and disillusionment with President Barack Obama’s leadership, the domestic agenda dominated the campaign.

But don’t be fooled: there is a strong undercurrent of debate that can have a big impact on America’s world view. Also, don’t assume that the divisions on these issues always break neatly according to party lines. Some Democrats and Republicans describe what has gone wrong in the world in eerily similar terms. With the Republicans controlling the new House of Representatives and the Democrats the Senate, there could be surprising alliances.

True, there will be predictable battles. The Russians have good reason to be worried about the fate of the new Strategic Arms Reduction Treaty signed by Obama and Russian President Dmitry Medvedev in April. The administration needs to get the support of 67 senators to ratify the agreement in the lame-duck session. If it fails to do so then, this centerpiece of the U.S.-Russia “reset” in relations could be doomed. Similarly, Cuban-born Florida Republican Rep. Ileana Ros-Lehtinen, in line to take over the House Foreign Affairs Committee, is likely to apply the brakes to any effort by Obama to ease sanctions on Cuba. She and other Republicans also have warned against any weakening of American backing for Israel.

When Democrats and Republicans echo each other, it doesn’t necessarily make for good policy, though. During the campaign, Democrats—tied to the trade unions and prone to protectionism—bashed Republicans for their business links to China. Senate Majority Leader Harry Reid attacked his Tea Party opponent, Sharron Angle, for “outsourcing to China and India.” Republican John Boehner, the presumptive House speaker, charged that Obama’s stimulus package “shipped jobs overseas to China instead of creating jobs here at home.” Not exactly elevating rhetoric from either side.

Where left and right agree is that America feels adrift right now. George W. Bush was seen as pursuing single-minded policies that polarized the country and the world; Obama seems not to be sure what he wants to do to change the perception that America’s best days may be in the past. Even once enthusiastic supporters see him as equivocating at every step.

Many Republicans argue that Obama has abandoned the idea of “American exceptionalism.” California Rep. Howard P. “Buck” McKeon declared earlier this year that he yearns “for the days of an American president who proclaimed around the world that America is a ‘shining city upon a hill.’ ” The Republican charges that Obama has embraced a “declinist vision.”

Some on the other side of the spectrum agree with the premise that America is in decline. “We really have become a modern-day Gulliver—tied up by small, determined powers whose interests aren’t our own,” writes analyst Aaron David Miller at ForeignPolicy.com. He urges Obama to keep “his ambitions small” and steadily decrease the U.S. role in conflicts like Afghanistan, where Miller sees no possibility of winning.

The Democratic left may feel diminished American power isn’t a bad thing, and the Republican right may resent it, but both often conclude that the country should avoid “foreign entanglements,” as George Washington famously put it. It’s a vision of a more isolated America, trying to keep the world’s problems at bay. Savvier politicians understand that the big -problems—everything from economic troubles to terrorist threats—cannot be cordoned off, and in a divided Congress, their voices could be heard. If Obama wants bipartisan successes, he could reach out to the Republicans who still support free trade, tempering the shrill rhetoric on both sides. If Republicans want to disprove the charge that they are the Party of No, they can suggest specific ways to bolster American power—for instance, by working with the Obama team on ensuring an effective ballistic-missile-defense system. Washington needs leaders who understand the world, and don’t run from it.