Eisenhower's "civilian" versus "military" distinction is mostly revisionism. Even astronautix.com can't decide whether the Viking was a civilian or a military rocket. There was indeed a rocket rivalry between the branches of the armed services (Army: Jupiter, USAF: Atlas), but Eisenhower wanted the satellite launched on a booster of American design, lest the victory be tempered by an accusation that it was really a German rocket. It was well known that the Jupiter was almost exclusively a German design while the Viking was American. I don't think the Atlas was ever seriously considered.

The Vanguard first stage was adapted from the Navy Viking. The second and third stages were similarly cobbled together from various vehicles not yet associated with any particular armed force. The whole thing was duct-taped together and unsuccessfully tested numerous times.

The Viking by itself was a successful design. The upper stages evolved into successful Air Force rocket stages. The parts were okay, but they just weren't destined to work together.