WASHINGTON — In the next four years, President Barack Obama has a war in Afghanistan to end, a defense budget to balance and a legacy of diplomacy and national security to shape.

Even before he took his second oath of office on Monday, budget fights on Capitol Hill threatened to do all his legacy shaping for him.

Obama hasn’t managed to shepherd a budget through Congress since 2009 and is facing another government shutdown threat in less than a month. Even with a debt ceiling compromise, lawmakers will need to find fixes for billions in automatic federal spending cuts by the end of March, something they haven’t been able to compromise on over the last two years.

So while old headaches like Iran and North Korea intersect with new threats like Mali and Algeria, military watchers are left wondering just how the White House will balance domestic fights with long-term security concerns — and how much money they’ll have for either.

The president acknowledged the connection in his inauguration remarks Monday, albeit in a more positive light.

“A decade of war is now ending,” he said. “Our economic recovery has begun. America’s possibilities are endless.”

The president also referenced the upcoming fiscal fights, but not the Pentagon budget specifically.

Significant cuts to military funding were a certainty after Obama won re-election in November, according to Elizabeth Sanders, professor of government and politics at Cornell University.

“It could well be an important transition in that respect, and with regard to an emphasis on diplomacy rather than military interventions,” she said.

Obama on Monday promised to uphold American values “through strength of arms and rule of law,” reinforcing that diplomatic approach.

“We will show the courage to try and resolve our differences with other nations peacefully, not because we are naive about the dangers we face, but because engagement can more durably lift suspicion and fear,” he said.

But maintaining that path depends on how those defense cuts go into effect. One year ago, Obama’s Pentagon appointees outlined almost half a trillion dollars in spending reductions for the armed forces over the coming decade.

Republicans have protested that his vision of a leaner, more agile fighting force is unrealistic, given the continued demands of Afghanistan and the persistence of terrorist groups worldwide. But they’re also driving the push for meaningful debt reduction, something Democrats say must involve smaller postwar defense budgets.

More concerning to both groups is another $500 billion in defense reductions mandated under sequestration, set to go into effect in March after a last-minute reprieve earlier this month. Defense Secretary Leon Panetta has referred to the plan as a “goofy meat axe” that seriously jeopardizes military readiness.

Failure to find a compromise on that will mean reductions in nonwar programs and massive layoffs among defense civilian employees. In a memo last week, the Joint Chiefs of Staff wrote that “Should this looming readiness crisis be left unaddressed, we will have to ground aircraft, return ships to port and stop driving combat vehicles in training.”

But even a new deal is expected to bite deeper into the Pentagon’s wallet, creating challenges across the force.

Obama on Monday promised to “support democracy from Asia to Africa, from America to the Middle East, because our interests and our conscience compel us to act on behalf of those who long for freedom.”

Balancing resources for that will fall to Obama’s pick for his third defense secretary, former Nebraska Sen. Chuck Hagel. He’s a fiscal conservative with concerns about past overuse of fighting forces in foreign policy, a politician whose views dovetail nicely into the more diplomacy, less intervention approach.

Assuming he’s confirmed, Hagel will oversee the end of combat operations in Afghanistan and the expansion of military coordination with allies across the globe, with an emphasis on the Pacific region.

Lyn Ragsdale, dean of Rice University’s School of Social Sciences, said the campaign slogan of Obama as “the man who ended the wars” may not have much historic staying power, but the overall foreign policy shift toward diplomacy may.

Obama has already received a Nobel Peace Prize for his foreign policy philosophy, a direct contrast from the international perception of George W. Bush’s authoritarian approach.

A study by the Brookings Institution last month found that two-term presidents generally replace the swing-state campaign stops of the first four years with international travel and a stronger focus on those foreign policy concerns.

Researchers said since Obama’s domestic policy goals will likely be stifled by ongoing Capitol Hill gridlock, those international issues may be the only realistic area where he can cement a presidential legacy.

But Sanders said the military’s heavy use of drone warfare — with Obama’s blessing — somewhat undercuts the kinder, gentler foreign policy narrative.

“John Brennan’s appointment (to lead the CIA), which the president seemed to think would sail through, brings up all the doubts about drones, torture, civil liberties, and human rights,” she said. “I think these policies, the continuation and extension of Bush claims and actions, will be more definitional for Obama than the very long process of ending the wars.”

But the president made the end of the war in Afghanistan a key point in his inauguration speech, calling on all Americans to remember both the triumph and pain of the last 12 years.

“We, the people, still believe that enduring security and lasting peace do not require perpetual war,” he said.

“Our citizens, seared by the memory of those we have lost, know too well the price that is paid for liberty. The knowledge of their sacrifice will keep us forever vigilant against those who would do us harm.”

“But we are also heirs to those who won the peace and not just the war, who turned sworn enemies into the surest of friends. We must carry those lessons into this time as well.” Twitter: @LeoShane

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