In order to identify the direct object (D.O), you should be able to identify verb patterns. In "with the advent of the space shuttle program, (...)", the main verb is "to spend".
"To spend" is a transitive verb which selects two complements: an NP subject of the sentence and an NP object, in this case (somebody spends something). Therefore, the NP NASA functions as the subject of the sentence; while, the direct object is represented by the NP "more time on military projects".
