Interesting topic... let's see what would happen.
1968: With the American landing of astronauts on the moon imminent and the Soviet lunar program in shambles, the Soviets decide to secretly work on sending a human to Mars, permanently.
1969: The N1 rocket spectacularly lifts off in a completely successful maiden flight.
1976: The even larger derivative of the N1, the N2, lifts off in a flawless maiden flight.
1976: NASA and the CIA think that the Russians are planning to send a larger spacecraft to the Moon with more people and establish a moon base.
1976: A fiscally responsible Congress and White House refuses to give NASA funds for continued Moon/Mars exploration, and asks that it focus on LEO stuff. Most people assume that the Soviets are just planning a big space station, or maybe a manned moon mission.
1981: An N2 rocket launches from Baikonur Cosmodrome, containing four cosmonauts, their "Mars house" and their life-support systems. Plans are to send additional N1 rockets repeatedly to send them supplies and spare parts once they land on the Red Planet.
1981: The Soviet Union announces its grand mission to Mars, when most people weren't expecting it.
1981: The Western world freaks out, realizing that it has been beaten in the space race. People start sketching plans for manned trips to Mars, the Asteroid Belt, Jupiter, and Venus. President Jimmy Carter, however, remains adamant that space exploration should be for the sake of science, and ramps up funding for unmanned space exploration.
1982: The cosmonauts are only 0.1 AU away from Mars when a coronal mass-ejection kills all of them.