The third pot of potential wall money would be $2.5 billion drawn from a military counterdrug account under a different statute — one that does not involve any emergency declaration. In it, Congress has authorized the Pentagon to support other agencies’ counternarcotics efforts by constructing “roads or fences and installation of lighting to block drug-smuggling corridors across international boundaries of the United States.”

On its face, the statute appears to authorize spending only for construction. If it cannot be stretched to encompass land acquisition, the $2.5 billion would most likely be useful only for building barriers on property the government already owns. Either way, time is short. Mr. Shanahan said that “the money that could be reprogrammed for counterdrug is money that would have to be spent in this year.” The fiscal year ends on Sept. 30.

Does the military have $2.5 billion in counterdrug funds?

No. When Congress passed the most recent Pentagon spending law last September, it appropriated about $517 million for counternarcotics support activities. Of that amount, about $100 million remains readily available for border barrier spending, an administration official said.

Where will the rest come from?

The Trump administration plans to use the counterdrug account as a temporary way station for more than $2 billion in funds taken from unrelated military programs. The administration will first transfer the funds into the counterdrug account, and then treat them as money that can be used for border barriers.

But the Defense Department has not yet decided which other programs to drain of their funding.

One military official, speaking on the condition of anonymity to discuss internal deliberations, said the Pentagon had been scouring its $700 billion budget in search of accounts with unspent funds to target. For example, the official said, an Army personnel account designated for paying bonuses to new recruits appears to have excess money because the service has been falling short of its recruiting goals lately.