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It appeared to be a classically braggadocios claim from President Donald Trump: The new administration’s budget for 2018 would add $54 billion to the defense budget, “one of the largest increases in national defense spending in American history," the president claimed in his first address to both chambers of Congress.

But the numbers — as well as the history — don’t quite add up, experts say.

“It’s an Obama-esque budget with a Trump-sized sales pitch,” Paul Scharre, senior fellow and director of the Future of Warfare Initiative at the Center for a New American Security and Iraq War veteran, told NBC News.

Mark Cancian, senior adviser to the CSIS International Security Program and a former division chief at the Office of Management and Budget, said “it took about half a day to figure out where the $54 billion came from. After half a day, it became clear that they were measuring from the budget control caps, so it’s really an increase from a decrease.”

President Barack Obama signed the Budget Control Act in 2011, which capped federal spending until 2021. The legislation is a result of a compromise between Democrats and Republicans, and says that defense programs can't grow without comparable investment in domestic social programs.

Proponents say these caps have become a significant impediment to expand military spending and have brought down defense expenditures in recent years. Opponents say the caps have led to dangerous personnel and equipment shortfalls and are asking Congress to repeal the limits on defense spending.

"So the increase is not as large as people were expecting," Cancian added. “Obama had proposed an increasing of something like $35 billion above the caps, and Trump is proposing another $18 (billion) or so."

In the budget plan shared by the White House, the Trump administration attempted to sell their proposal as a 10 percent increase for fiscal year 2018. The administration said it would pay for the increase by making large cuts to the State Department and Environmental Protection Agency.

On Monday, 120 three- and four-star generals and flag officers stated their concern about cuts to the State Department and Foreign Affairs Budget.

Related: Trump Budget Plan Boosts Defense Over Safety Net, Diplomacy

“As Secretary James Mattis said while Commander of U.S. Central Command, ‘If you don’t fully fund the State Department, then I need to buy more ammunition',” they wrote. “The military will lead the fight against terrorism on the battlefield, but it needs strong civilian partners in the battle against the drivers of extremism — lack of opportunity, insecurity, injustice and hopelessness.”

Retired Gen. George Casey, who signed the letter and served as Army Chief of Staff from 2007 to 2011, was at Capitol Hill the day Mattis made that statement.

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Mattis and Casey, who also led all coalition forces in Iraq from 2004 to 2007, spoke to a group of U.S. senators after a recent cut to defense funding.

"I started my comments to the senators by saying that it might seem like a bit of an anomaly to have a military guy here arguing for the State Department budget after the military budget just took a big cut, but that’s how important it is," Casey said.

"It’s an essential part of cementing the success of the security operations," he added.

The $54 billion defense increase the Trump administration is budgeting for is also slightly misleading, according to University of Denver Finance Professor Andy Sherbo, who previously served as the CFO of the Pacific Air Forces.

“They’re trying to sell it as a 10 percent increase, but it’s not,” said Sherbo.

The $603 billion Trump proposed for fiscal year 2018 in the budget is for “Defense-Related Spending,” which is not just for the Defense Department. This spending category is comprised of the Pentagon, as well as all other federal agencies, including the Department of Energy’s oversight of the country’s nuclear arsenal.

The Obama administration’s defense budget for 2018 would be bumped to $584.7 billion if “Defense-Related Spending” were taken into account, according to the United States Naval Institute.

Sherbo said this shrinks the difference between Trump and Obama’s budget to $18.3 billion, or 3.1 percent — a paltry sum to defense hawks.

Senate Armed Services Chairman John McCain, R-Arizona, who called for a 2018 defense budget of $640 billion that would increase to $800 billion by 2022, noted as much in a statement.

“In other words,” McCain said, “President Trump intends to submit a defense budget that is a mere 3 percent above President Obama’s defense budget, which has left our military underfunded, undersized, and unready to confront threats to our national security.”

Texas Congressman Mac Thornberry, the Republican chair of the House Armed Services Committee, agreed with McCain, adding another wrinkle to the Trump administration's budget proposal.

Scharre also agreed. “They’re not going to have enough money to grow the force to the size they want and modernize in the way the Pentagon needs to,” he added.

Related: Trump Wants to Make U.S. Nuclear Arsenal ‘Top of the Pack’

Trump said that his plan to expand the military would grow the current fleet to 350 ships, train tens of thousands of new soldiers and Marines and significantly increase the number of combat aircrafts. Experts doubt that $18 billion will get the military there.

The Pentagon’s newest class of aircraft carrier, released in 2016, cost $12.9 billion alone.

"This won’t get him close to his goal,” Sherbo said. “Maybe his thought process is that the Pentagon will be able to cut procurement costs.”

“But the 3.1 percent is not a noticeable increase,” he added.

According to Scharre, it is possible to use the current budget to shape the armed forces to reflect Trump’s plan. It would, however, require political capital.

“If you’re willing to take cuts in politically fraught areas — increase Tricare [military health insurance] fees for retirees, close unnecessary military bases — then you can probably afford the military we need within this budget,” Scharre said.

Despite some military leaders’ issues with Trump’s budget proposals — the cuts to the State Department and the disappointment in the defense increase — Cancian said that it’s still early to draw too many conclusions.

The Trump administration is set to release its "skinny budget" and five-year defense plan, he said, which will provide greater detail.

But Casey has a greater concern: the politicization of the defense and foreign aid budgets.

"It’s my gut feeling that the people this administration is catering to believe we shouldn’t give any foreign aid — they think the foreign aid budget is 20 percent of the budget," he said noting that it's less than 1 percent. "I just hope they're not playing to that base and focus on accomplishing our diplomatic missions abroad."