Analysts said the differences stem from a deep philosophical divide. One camp, bolstered by military officers who say the debt is a major national security issue, argues that slowing spending now will create a stronger America in the future.

But Mr. Romney’s side argues that the U.S. can’t foster the kind of stability that is needed around the world without maintaining a powerful and well-funded military in the near term, said Jim Talent, a former Republican senator from Missouri who once served on the Senate Armed Services Committee and is a special adviser to the campaign.

It’s the classic “peace through strength” philosophy, said Mr. Talent. He said global stability fosters economic growth, which benefits U.S. businesses, who then pay more in taxes because they are more prosperous.

“There’s a price to strength, but there’s a greater price to weakness,” he said. “When you don’t adequately fund the military, you end up increasing the amount of risk of security around the world, which tends to suppress economic growth.”

While the campaign resists discussing specific dollar amounts, Mr. Talent and others speaking for the Romney camp assert that core defense spending must be set at a floor of 4 percent of the nation’s gross domestic product.

Based on the White House Office of Management and Budget’s GDP projections, a Romney administration would fork out roughly $800 billion toward national defense in 2016 — a notably higher amount than the trimmed-down $578 billion proposed by the Obama administration.

Different as they may be, both figures represent a doubling of whatCongress allowed during the years before the Sept. 11 attacks.

Some have asserted that neither Mr. Obama nor Mr. Romney has a real plan for reining in runaway defense spending.

“Obama will spend a lot; Romney will spend more. That’s the difference,” said Winslow T. Wheeler, an analyst at the liberal Center for Defense Information, who worked on national security issues for 31 years for members of the Senate from the end of the Vietnam era through the Sept. 11 attacks in 2001.

Defense spending as a percentage of GDP, which is how many on Capitol Hill measure it, shrank by half after the end of the Cold War, to a low of 3 percent in 2001. It has been rising since and reached 4.7 percent in 2011.

Not everyone agrees that the GDP yardstick is worthwhile.

“Pentagon spending is high right now when you measure it in dollars, but they’re measuring it against the GDP, which is rubber,” he said, noting that the two don’t always grow and shrink at the same rate.

“If one thing has grown faster than the other, you can pretend the other thing has grown lesser, but it’s actually grown bigger,” said Mr. Wheeler, who contends that the Romney camp is preying on such confusion in an attempt to portray Mr. Obama as a man bent on gutting the Pentagon.

Take the Navy, which plans to build nine ships a year for the next three decades at a cost of at least $20 billion a year, or $599 billion through 2042.

Mr. Romney says he wants to increase that to 15 per year, which, according to Congressional Budget Office estimates, would increase the annual budget to $33.5 billion a year, nearly doubling costs over the next 30 years to $1.005 trillion.

The defense spending debate in Washington these days is dominated by talk of the sequesters — the automatic spending cuts set into motion by last year’s debt deal. On Jan. 2, the administration must make $110 billion in cuts, split between defense and domestic spending, with more cuts each year through the end of the decade.

Those cuts come on top of $487 billion in lower defense spending that the Obama administration already has proposed over the next 10 years.

Mr. Obama’s approach aims to “pave the way for more robust defense spending down the road,” said Michael E. O’Hanlon, a senior fellow at the Brookings Institution.

He said it’s a balancing act: Too many defense cuts too quickly could put the nation’s global security posture at “risk in the short term.”

Indeed, the Romney camp pulls no punches in the fight against proposed cuts. “It will be a priority to undo President Obama’s defense cuts in the first term,” said John Noonan, a defense policy adviser for the campaign.

Mr. Noonan, who has served as a House Armed Services Committee staffer under Rep. Howard P. “Buck” McKeon, California Republican, said current defense spending “is at historic lows if you look at historic trends.”

“If President Obama’s defense cuts continue on their current trajectory, then it goes down to somewhere in the high 2 percent range of GDP.”

Progressives, some of whom have Reagan Republican pasts, tell another story. They say Mr. Obama’s proposals are portrayed inaccurately by the Romney camp and are a result of calls from both major political parties to rein in the post-Iraq War defense budget while tackling the deficit crisis.

“What Obama has done is reduce the projected growth in defense spending. It’s not actually a cut,” said Larry Korb, who was an assistant secretary of defense under President Reagan. “Let’s say you’re making $50,000 a year, and I tell you that in 10 years, your salary will be $100,000, but the economy is in a downturn, so actually I’m only going to give you $80,000 in 10 years.”

“Compared to what Eisenhower did after Korea, or Nixon did afterVietnam, or if you look at Reagan’s second term when we cut defense by 10 percent in four years, the Obama $486 billion is not that big of a cut,” he said. “It’s 8 percent over 10 years.”

The irony, said Mr. Korb, now a senior fellow at the left-leaning Center for American Progress, is that “apart from the first Reaganadministration, the Pentagon has historically made out better under Democrats than Republicans in terms of money.”

“And the problem with Romney saying he’s going to increase defense spending,” said Mr. Korb, “is how is he going to do that while also dealing with the deficit?”