Acting Defense Secretary Patrick M. Shanahan said this weekend that he will make the final call on $3.6 billion in military construction money that President Trump wants to build his border wall and quickly shot down the notion of raiding any funds meant to build or repair housing for troops and their families.

The Pentagon chief — who wouldn’t even commit to giving the White House all the money it wants under the president’s national emergency declaration — is pushing back as speculation swirls that key military projects at home and abroad could be on the chopping block.

Lawmakers in both parties spoke out forcefully Sunday to try to save projects that they say are now at risk, and the acting defense secretary seemed well-aware that he has been thrust into the middle of a politically charged battle that pits border security against military spending, two central priorities of the Republican Party.

“I think I have a lot of discretion,” said Mr. Shanahan, who took over the job on Jan. 1 after a 30-year career at the defense contracting firm Boeing. “I’m not required to do anything.”

Upgrades to a U.S. military hospital in Germany; dock repairs at Pearl Harbor; the operation of a middle school at Fort Campbell, Kentucky; flight training projects at military facilities in Texas; and maintenance at other bases across the country and across all branches of the armed forces could have funding slashed or eliminated entirely. Mr. Trump’s emergency declaration Friday gives him access to a pool of roughly $21 billion in unspent military construction funds to use for the wall.

White House officials said they will try to pull about $3.6 billion out of that pot. The rest of the roughly $8 billion needed for the border barriers will come from money allocated last week under the bipartisan spending deal, military counternarcotics programs and a Treasury Department forfeiture program.

But Defense Department officials, along with lawmakers of both parties, are resisting the idea of siphoning military construction funds.

Mr. Shanahan would not commit to the $3.6 billion figure. He said he needs to sit down and review all projects on the table. The Pentagon was prepared for the emergency declaration, he said, and crafted a process to begin examining the construction budget.

“Very deliberately, we have not made any decisions. We’ve identified the steps we would take to make those decisions,” Mr. Shanahan told reporters while traveling back to Washington from a NATO conference in Brussels. “This is the important part of that. We laid that out so we could do it quickly. We don’t want to fumble through this process.”

Mr. Shanahan already has ruled out at least one area of the military construction budget. Pressed by reporters on whether he could promise housing for troops would be protected, the acting secretary offered strong assurances.

“Will we take care of our men and women? ‘Yes’ is the answer,” he said.

Projects outside of military housing, however, could be targets.

One area reportedly under consideration is a school at Fort Campbell. Lawmakers who back the president’s proposed wall and emergency declaration said upgrades and operational costs for the school ultimately will be funded but that the students would benefit equally from a stronger border.

“I would say it’s better for the middle school kids in Kentucky to have a secure border,” Sen. Lindsey Graham, South Carolina Republican, told CBS’s “Face the Nation” on Sunday. “We’ll get them the school they need. Right now, we’ve got a national emergency on our hands.”

Similar projects, such as a child development center at Joint Base Andrews in Maryland, also reportedly are getting a second look.

The money at issue comes from “unobligated” funds in defense budgets over the past five years. The money has been designated for specific military projects, but no contracts have been signed and the construction or repairs have yet to begin.

While Mr. Graham defended the president’s strategy, other Republicans argued that their party has spent the past two years fighting for more money for the military. Pulling money from the military budget, they said, would be a mistake and could hurt the readiness and training of American troops.

“How about the fact that in my district, in Del Rio, Texas, this produces more pilots than any other facility in the United States of America?” Rep. Will Hurd, Texas Republican, said of Laughlin Air Force Base.

“If it rains more than an inch, the flight line gets flooded and they can’t train. We’ve been working on fixing that. … That’s a good place to spend that kind of money rather than trying to build a wall,” Mr. Hurd told CBS. “I don’t want to see that money being taken away from that.”

Sensing a political opportunity to drive a wedge between the president and Republicans on Capitol Hill, Democrats zeroed in on specific military projects that could now be shelved. They cited those projects in their pitch to Republican colleagues to back a congressional resolution formally disapproving of Mr. Trump’s emergency declaration.

“I think there’s enough people in the Senate who are concerned that what he’s doing is robbing from the military and the DoD to go build this wall that, you know, is really not even the best way to fight the crisis,” Sen. Tammy Duckworth, Illinois Democrat, said during an interview on ABC’s “This Week.”

“Let me tell you the kind of things that are on the table to be chopped right now,” she said. “Crash-and-rescue station in Peoria, Illinois, at the airport that I flew out of as a helicopter pilot for 15 years — that’s on the table. Training, construction of training rifle ranges, where we send our troops to become marksmen so that they can be more lethal on the battlefield. Recovery efforts in places like Tyndall Air Force Base, places where we’re recovering from hurricanes. Pads and hangars for the new F-35 fighter jets.”

With the exception of Mr. Graham, most Republicans seemed reluctant to defend pulling money from specific military projects even as they backed Mr. Trump’s broader goal.

“It’s not my decision,” said Rep. Jim Jordan, Ohio Republican and co-founder of the conservative House Freedom Caucus.

“It’s going to be a decision by those people in the military and the administration and the president of the United States,” he told ABC News on Sunday.