WASHINGTON—Rep. John Garamendi is known as a staunch advocate for cutting unnecessary defense spending. But the California Democrat avidly defends one program: a fleet of high-altitude surveillance drones that the Pentagon wants to scrap.

While Mr. Garamendi says the drones are a critical Pentagon tool, there is another reason he is a vociferous defender of the unmanned aircraft: Pilots who control them work at a base in his congressional district.

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