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I think Nikita Khruschev inspired Eisenhower more than the Autobahn.
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Although the primary justification for the Interstate System involved civilian benefits, its value for defense purposes was another important factor. A particular concern was the need to evacuate cities if an atomic bomb were on the way.
In the 1950's, the issue of evacuation was not in any sense frivolous at the height of the Cold War with the Soviet Union. For example, while President Dwight D. Eisenhower began lobbying congressional leaders on behalf of the highway proposal he would submit on February 22, 1955, he was preoccupied with the Formosa Straits crisis that erupted when the People's Republic of China appeared ready to cross the straits and attack Chinese Nationalists on Formosa (now called Taiwan) over control of the islands of Quemoy and Matsu.
This was a major international crisis, as illustrated by Eisenhower biographer Stephen E. Ambrose's observation that, "the United States in early 1955 came closer to using atomic weapons than at any other time in the Eisenhower Administration."
For the President, the Formosa crisis illustrated the need for the Interstate System. He worried about evacuating Washington and other cities in the event of a nuclear attack. He knew the present roads were inadequate for that purpose.
Still, in a meeting with legislative leaders on January 11, 1955, the Formosa crisis prompted a discussion of what would happen in the event of a nuclear attack on the United States. The President said he was worried about an atomic bomb attack, which prompted him to suggest the need for a plan to relocate Congress in an emergency.
https://www.fhwa.dot.gov/infrastructure/civildef.cfm
