As the four armed forces chiefs testified in the Senate about the national security dangers of mandated budget caps, Sen. Lindsey Graham asked each officer if he had discussed the readiness crisis with President Obama.

Their unanimous answers before the Senate Armed Services Committee last week underscored a key aspect of the Obama presidency, noted by his own past defense secretaries and, in a recent disclosure, a former NATO commander: The president maintains a wary approach in dealing with the four-star generals and admirals who direct his wars.

“Have you told the president what you’re telling us about the state of the military under sequestration?” asked Mr. Graham, South Carolina Republican. “Have you had a conversation with the commander in chief, telling him what you just told us?”

Army Gen. Mark Milley was the first to answer. “I have not personally had a conversation.”

As Mr. Graham’s roll call continued, Navy Adm. John Richardson, Marine Corps. Gen. Robert Neller and Air Force Gen. David Goldfein gave the same answer: “No.”

Republican presidential nominee Donald Trump said this month at an NBC News forum that generals have been “reduced to rubble” by Mr. Obama. Although that may be Trump hyperbole, the president’s own political appointees acknowledge a problem.

Robert M. Gates, Mr. Obama’s first defense secretary, wrote in his memoirs that Mr. Obama deeply distrusts senior military leaders and suspects them of conspiring against him. He recalled one meeting in which the president resorted to a clipped “That’s an order” to the top brass.

“That order was unnecessary and insulting, proof positive of the depth of the Obama White House distrust of the nation’s military leadership,” a “shocked” Mr. Gates wrote.

“The controlling nature of the Obama White House and the staff took micromanagement and operational meddling to a new level,” he said in his memoir, “Duty.” “I think Obama considered time spent with generals and admirals an obligation.”

Mr. Gates’ successor, Leon E. Panetta, wrote in his memoir, “Worthy Fights,” that the White House — read Mr. Obama — saw generals who swayed from its talking points as conspirators. One incident involved a disagreement over troop levels in Afghanistan.

“The White House saw this as a coordinated effort to limit the president’s decision space, while Gates saw it as evidence that the Pentagon brass was unable to stay on message,” Mr. Panetta wrote. “For my part, it seemed that the leading generals saw the problem the same way and weren’t good about keeping quiet, but not that they were organizing a campaign against their president.”

Army Gen. Stanley A. McChrystal ended up getting fired by the White House as the top commander in Afghanistan after he disagreed publicly with the strategy and his staff made unkind remarks about senior officials in a published story.

Retired Army Lt. Gen. Michael T. Flynn, a close adviser to Mr. Trump, said he was fired by Mr. Obama as director of the Defense Intelligence Agency because he pushed for identifying the terrorist threat as radical Islam and for wanting to do more about it. Mr. Obama refuses to link Islam the religion with terrorism.

Mr. Flynn defended Mr. Trump’s “rubble” characterization on “Fox & Friends.”

“He’s absolutely right. There’s a severe disconnect between this White House and frankly the president and our military,” the former intelligence chief said. “I mean, there’s a lot of frustration within the ranks, and there’s a lot of frustration I know in the senior leadership about what we’re not able to do.”

Democratic presidential nominee Hillary Clinton immediately criticized Mr. Trump’s “rubble” remark and, in effect, defended Mr. Obama’s handling of his generals.

“It’s hard to forget what Trump did last night,” Mrs. Clinton said in a campaign speech. “It was a test, and he failed it. He trash-talked about America’s generals, saying that they’ve been, quote, ‘reduced to rubble.’ He suggested he would fire them all and hand-pick his own generals since, you know, he knows so much about what it takes to be a general. He attacked dozens of former flag officers.”

Mrs. Clinton recounted Mr. Obama’s careful discussions with top military and national security leaders before approving the raid that killed Osama bin Laden in 2011.

Mrs. Clinton, as Mr. Obama’s first secretary of state, also accused Mr. Trump of being “unpatriotic” for what she claimed is his preference for Russian President Vladimir Putin over the U.S. president.

The Obama administration is fresh from negotiating a cease-fire agreement with the Putin government for Syria and setting up a joint Russian-U.S. command center.

As a senator in 2007, Mrs. Clinton famously ridiculed the testimony on the Iraq troop surge from Army Gen. David Petraeus.

“You have been made the de facto spokesman for what many of us believe to be a failed policy,” Mrs. Clinton said. “Despite what I view as your rather extraordinary efforts in your testimony both yesterday and today, I think that the reports that you provide to us really require a willing suspension of disbelief.”

Another four-star casualty in the Obama years is retired Marine Corps Gen. James Mattis, who was pushed out by the White House as chief of U.S. Central Command because of his hard-line view toward Iran, according to congressional observers. The White House wanted a nuclear deal with Tehran and wanted Gen. Mattis’ voice silenced, the sources say.

An Aug. 10 report by a joint House panel on CentCom intelligence-skewing said Gen. Mattis “was forced to depart abruptly in early 2013.”

“The leadership environment within CENTCOM and its Intelligence Directorate deteriorated significantly following the 2013 departure of Marine General James Mattis and his senior intelligence leaders,” the report said.

In retirement, Gen. Mattis has been a sharp critic of the strategy to defeat the regional threat of the Islamic State, which controls territory in Syria and Iraq and has set up and inspired terrorist armies in at least six nearby nations.

In April, Gen. Mattis said the Iran deal “fell short” by merely delaying, but not eliminating, Iran’s timetable for building nuclear weapons. He said Shiite-theocratic Iran is “not a nation state, but a revolutionary cause intent on mayhem.”

Gen. Mattis is not the only combatant regional commander who disagreed with the White House.

Recently retired Air Force Gen. Philip M. Breedlove, who commanded NATO, was having so much trouble in even talking with the White House that he asked former Secretary of State Colin L. Powell to intercede. His intermediary was Harlan Ullman, a longtime Washington military analyst.

His email conversations were obtained by the hacking group DCLeaks.

Gen. Breedlove, then in command, wrote to Mr. Powell: “Thank you for this. Sorry for the tardy reply. I know Harlan has passed some of my proposed ‘asks’ of you. Let me add one thought. I may be wrong but I do not see this WH really ‘engaged’ by working with Europe/NATO. Frankly I think we are a ‘worry’ ie a threat to get the nation drug into a conflict vice an ‘opportunity’ represented by some pretty stalwart allies. I seek your counsel on two fronts, how to frame this opportunity in a time where all eyes are on ISIL all the time, and two, how to work this personally with the POTUS. v/r Phil.”

At the Senate Armed Services Committee hearing last week, Chairman John McCain, Arizona Republican, said this year’s defense budget is $150 billion below the 2011 level because of “arbitrary” cuts mandated by the Budget Control Act.

“Rising threats and declining budgets have led to shrinking military forces that are struggling to sustain higher operational tempo with aging equipment and depleted readiness,” said Mr. McCain.

The service chiefs then laid out what Adm. Richardson called a readiness “whammy.”

“We are compromising the readiness of those ships and aircraft that we will have to surge to achieve victory in a large conflict,” he said. “And we have also curtailed our modernization in a number of areas critical to staying ahead of our potential adversaries.

Said Gen. Neller, “I believe we are now pushing risk and the long-term health of the force into the future.”

All four service chiefs said they will not have the capacity to defend the nation against all threats if automatic caps, called sequestration, continue.

Said Mr. Graham: “I will make some suggestions to you. Go tell the president what you’re telling us. I absolutely see the flaws in what the White House is doing.

“I can’t believe the commander in chief is sitting on the sidelines and watching this happen, taking a laissez-faire attitude that, if you send me a bill that increases defense spending without increasing non-defense spending, I will veto it,” the senator said. “I find that is repugnant as what the White House is doing.”

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