A UH-60 Blackhawk helicopter drops off a U.S. soldier for a mission near Jalalabad, Afghanistan, on Dec. 20. Obama’s budget proposal, and the ensuing battles, could be a preview of the national security debate in the 2016 presidential election. (Lucas Jackson/Reuters)

The battle over the budget that President Obama will submit Monday is emerging as a preview of the 2016 presidential election debate on national security, an area that for now appears to be the greatest vulnerability of Obama and the Democrats.

The president will ask Congress to break through its own spending caps — commonly referred to as “sequestration” — and allocate about $561 billion for Pentagon expenditures, about $38 billion more than is currently allowed under the law.

There’s broad consensus in both parties that the military needs more money to modernize its forces and meet its responsibilities in a world that seems to have grown more chaotic and dangerous in the past 12 months. It’s unclear, however, how Congress and the White House can come to an agreement on where to find the additional funds.

Even if both parties share the blame, a cash-strapped Pentagon could still provide an opening for Republicans — whose standing on national security issues was damaged by the Iraq war — to make an argument that they are the party best positioned to keep the country safe.

“A lot of Republicans see opportunity in an election that’s a referendum on Obama’s foreign policy,” said Danielle Pletka, vice president for foreign and defense policy studies at the conservative American Enterprise Institute. A presidential election featuring Hillary Rodham Clinton, who served as Obama’s secretary of state, would raise the profile of international issues.

President Obama’s annual budget proposal includes a $4 trillion price tag, a 10-year deficit reduction plan — and almost no chance of passing a Republican-controlled Congress. Here’s what you need to know about his proposal and its political implications. (Julie Percha/The Washington Post)

Democrats, though, are determined to prevent the re­emergence of their pre-Iraq-war reputation as being the weaker party on defense.

The impasse over the defense budget has left the Pentagon’s top generals complaining that the spending caps, which have been in place since 2013, are damaging the military at a time when the country can least afford it. The list of new threats includes Islamic State fighters, who last year seized major cities in Iraq and Syria, a Russian-backed insurrection in eastern Ukraine and the collapse of the government in Yemen.

“The global security environment is more dangerous, and sequestration is still on the books as the law,” Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, said last week. “It’s absolutely crazy for this country.”

Obama has in recent months been able to cite a resurgent economy, strong job growth and a low unemployment rate as proof that his economic policies are delivering for the nation. “Because of the policies that this administration put in place, our economy has bounced back stronger than ever,” White House press secretary Josh Earnest told reporters Friday.

The public perception of the president’s handling of national security matters, amid the growing unrest in the Middle East and Ukraine, has not been nearly as strong. “We’ve had an interesting and, I would acknowledge, up-and-down year with respect to the perception of our foreign policy,” said a senior administration official who was not authorized to speak publicly ahead of the formal budget announcement.

In recent years, Republicans and Democrats have been able to blunt the worst effects of the budget caps by cobbling together short-term deals that modestly increased defense and domestic spending by finding offsets — essentially, cuts to other programs or fee increases. But each year that the budget caps are in place, it gets harder to find new savings to meet the Pentagon’s needs, lawmakers and White House officials said.

Republicans have shown little willingness to raise taxes to cover the costs of a bigger military budget. The White House, meanwhile, is not likely to back a budget compromise that would boost defense spending at the expense of prized domestic programs that have also been slashed in recent years.

“It looks like the administration is trying, but I don’t think the fundamentals are there for a compromise,” said Kathleen Hicks, who served as a top official in the Pentagon under Obama and now is a senior vice president at the Center for Strategic and International Studies.

Republicans, long divided between deficit and defense hawks, have not made additional spending on defense a top priority in recent years. But as the economy improves and the presidential election nears, they appear to be coalescing around the need for more Pentagon spending “for no reason other than expediency,” Hicks said.

“They’ll have to move to the center” on defense spending, she said. “And I do think world events are pushing them in that direction.”

It is unclear how hard the Obama administration is willing to fight for more military spending. Although the president’s blueprint includes a big boost for the Pentagon, some in the president’s party have questioned his commitment on the issue. The president did not mention the need for more military spending in his State of the Union address or in a major foreign policy speech at the U.S. Military Academy in late May— an omission that some hawkish Democrats found “worrisome,” Hicks said.

White House officials, though, insist that a failure to provide relief to the Pentagon would be devastating to the country’s military and its national security and that Obama will not accept a budget that carries the caps forward.

The promises of more money from Congress and the White House have yet to ease concerns in the Pentagon. The top brass have been complaining for years that the budget caps have forced them to pare back training, slash troop levels and gut their modernization programs.

Now their biggest worry is that lawmakers and the public have stopped listening to them on the issue and, absent a major crisis, will not fix the problem.

“At what point do we lose our soldiers’ trust, the trust that we will provide them the right resources, the training and equipment?” said Gen. Ray Odierno, the Army chief of staff.

The military’s case for more money also has been hindered by the turmoil at the top of the Defense Department.

Former defense secretary Chuck ­Hagel, who was essentially fired by Obama in November, had little background in Pentagon budget issues and generally seemed overwhelmed by the job, military officials said. Obama’s pick to replace him, Ashton B. Carter, has not been confirmed by the Senate. He has a long background serving at top levels of the Pentagon and is expected to be a more forceful and articulate advocate for lifting the budget caps.

Meanwhile, liberal Democrats, eager to fend off the Republican critique that excessive domestic spending and government waste have caused the Pentagon’s budget woes, cite the supporters of the 2003 Iraq war as the real problem.

“These are the same guys who voted for a war in Iraq and forgot how it was going to be paid for,” said Sen. Bernard Sanders (I-Vt.), a possible Democratic presidential candidate. “You know how it’s paid for? It’s paid for on the credit card. We don’t know how much it will cost by the time we take care of the last veteran . . . $3 trillion or $4 trillion. They weren’t worried about that.”

Missy Ryan and Steven Mufson contributed to this report.