It depends how you define a 'Mars Mission'.
A landing is really, really, really difficult, and requires a whole quantum leap beyond the technology possessed by either superpower until, well, now.
But going by the strictly literal interpretation of the question, a flyby is much easier. A flyby would probably be achievable by 1975--if, of course, there were any compelling reason to go...
In the EMPIRE studies of the early 1960s, flybys were proposed as a means of repairing and maintaining robotic probes. Unfortunately, as robots became more advanced, such a purpose became superfluous. Maybe less advanced robotics could lead to a Mars flyby program? Which, incidently, would be much easier than any other kind of mission.