Washington ? President Barack Obama ended one war and is winding down another, bringing home tens of thousands of U.S. troops. Now he wants them to pay him back — with votes.

“You stood up for America. America needs to stand up for you,” Obama told service members returning to Fort Bragg, N.C., from Iraq recently.

Expect to hear that pitch throughout the next year as the president’s campaign, mindful that large numbers of veterans and military families live in states crucial to his re-election chances, highlights his efforts to promote jobs and benefits for veterans returning from Iraq and Afghanistan. Republicans, meanwhile, already are countering his record, noting high unemployment among veterans.

The outreach to veterans is part of a larger effort by Obama to build inroads with voting blocs traditionally outside the Democratic umbrella while it tries to reactivate the coalition of women, minorities and young voters who helped propel him to the White House in 2008. Obama’s campaign is free to focus on building a diverse base of support for the general election because he faces no primary opponent. His eventual GOP challenger doesn’t have that luxury.

While Democrats have traditionally trailed Republicans on defense and national security matters, Obama senses an opening with veterans because he has generally received high marks from voters for his handling of terrorism — especially after the U.S. raid in May that killed Osama bin Laden — and in managing the U.S.’s relationships with other countries. A recent AP-GfK poll found that 59 percent of adults felt Obama would keep America safe, a mark that has remained steady throughout 2011.

Exit polls in 2008 showed that Obama received about 44 percent of voters who said they served in the military, while 54 percent voted for Republican John McCain, a former Navy pilot who was a prisoner of war for more than five years during the Vietnam War. Four years earlier, George W. Bush, who sought re-election as the U.S. waged wars in Iraq and Afghanistan, won 57 percent of voters who said they served in the military, compared with 41 percent for Democrat John Kerry.

There are obvious political reasons for Obama’s effort.

Several states that will be heavily contested next year have a significant military presence. Florida, home to a number of military installations, has more than 1.6 million veterans, according to the Veterans Administration. Virginia and North Carolina, political battlegrounds that Obama carried in 2008, both have about 800,000 veterans while Colorado, another important state in the Obama re-election calculation, has more than 400,000 veterans.

This year, the playing field in the fight to woo veterans may end up being level if anyone other than Texas Gov. Rick Perry and Texas Rep. Ron Paul — the only two with military experience in the GOP field — win the nomination. Obama had no military experience before becoming commander in chief. (The last time both parties didn’t have a presidential candidate with military experience was 1944, when President Franklin D. Roosevelt defeated Thomas E. Dewey.)

As the nation winds down wars in Iraq and Afghanistan, Obama and first lady Michelle Obama have held numerous events at military bases and in communities heavily populated by veterans. During a bus tour through North Carolina and Virginia in October, the president and first lady stopped at Joint Base Langley-Eustis in the heart of a large military community in Hampton and Newport News, Va. Since entering the White House, the first lady has held about 50 events with military families in 14 states.

Obama also has talked up his work on a new GI Bill helping veterans and service members to attend college and on tax incentives for companies that hire veterans, a piece of his jobs bill that won passage in Congress during the fall. The Democratic National Committee featured the incentives in ads that aired in North Carolina, New Mexico and Ohio.

Bob Wallace, executive director of the Veterans of Foreign Wars, said Obama has been “very positive” for veterans. He said members of his organization are looking for specific ways the next White House administration — Democrat or Republican — intends to help veterans.

“The cost of war continues after the last shot is fired and after you pull the trucks over the border into Kuwait,” Wallace said. “You’ve got a lot of expenses to take care of these guys and gals and that’s the commitment we’re looking for anybody who wants to be president of the United States.”