I second what Edlothiad suggested, Mars Direct would have been perfectly feasible. Mars Direct was created and proposed mainly by Dr. Robert Zubrin. His approach to a human Mars mission was precisely to find a way to do it using the available technology and not using technologies that are still in development or experimental, such as Nuclear Thermal Rockets, advanced propulsion, on orbit assembly, which would all drive up the costs. His research was initiated due to the 90-day report* and the very high costs associated with a more extensive and elaborate plan for going to Mars. He also suggested a mission that is as lean as possible, requiring the least amount of mass to be launched to make this possible with the class of launch vehicle technology available.
Some of the key points to his approach:
- Use available Saturn V/Shuttle class launch vehicle
- Launch, transfer, land and verify an unfueled return vehicle prior to crewed transfer
- Create propellant for return voyage on Mars with the Sabatier reaction using small amount of hydrogen and a small nuclear reactor brought from earth(ISRU).
- Transfer crew on direct orbit to Mars, no on orbit rendezvous, use a slower orbit that is safer due to it having a free return in case of emergency
- Land all crew on mars(no astronaut stays on orbit)
- Stay on mars for an extended time (due to conjunction orbit)
Zubrin has been pushing this approach for decades without any real movement from NASA. The main reason for this is that, due to multiple reasons, NASA is no longer driven to a singular goal, such as mars, and has many technology driven goals instead. To do humans to mars with the available budget even in this cost effective way would mean giving up on other programs such as ISS.
Some of the excuses given by opponents for why it would not work (or any other plan using available technology) are:
- We do not know how to deal with radiation, so more radiation research needed
- We want to go to Mars faster, so advanced propulsion needed
- ISRU has never been done so we cannot rely on it, so we need to bring fuel, so we need a huge ship and advanced propulsion
- The mass margins are too slim
Which can all be disproved, and have been, by Zubrin.
You can find multiple publications of this plan and the details such as:
http://www.marspapers.org/paper/Zubrin_1991.pdf
*Report of the 90 Day Study on Human Exploration of the Moon and Mars, 1989