Q:

Could "peak Apollo levels" of support have gotten NASA astronauts to Mars in the 1980's?

In an "alternate universe" where NASA continued to receive a mandate, funding and public support at say peak Apollo levels, could another ten or twenty years have gotten boots on Mars, with astronauts in those boots?
Or would there be some clear technical challenge that really needed several more decades of development before this would have been possible?
Ideally: a bit of math or some supporting links should be presented and not just an opinion or a list.
This question is motivated in part by this thoughtful answer.

A:

If you want to get really bummed out for 'what could have been', check out the Wikipedia page for List of manned Mars mission plans.
The earliest plan to get to Mars was written by von Braun in 1948, with the idea that we would be landing in 1965. With our current knowledge of Mars, it reads like science fiction. Seven passenger ships and three cargo ships would be assembled in Earth orbit using reusable shuttles to launch the materials. They would fly to Mars in the same way we do currently, at the optimal transfer window. They would find a landing site from orbit. A manned glider would be used to make the first landing on Mars, using skis to land on the polar ice cap. The crew would then travel overland using rovers and then build a landing strip.
http://www.astronautix.com/v/vonbraunmarpedition-1952.html
Obviously we now know much of this would be impossible. Mars doesn't have the thickness of atmosphere needed to support landing with gliders, and the radiation of interstellar space was completely unknown at the time. Additionally, the technology and engineering which would be needed to develop reusable shuttles were almost 30 years away, and even then NASA was unable to keep reuse tempos anywhere near what would be necessary for an extended space construction project.
Quick budgetary baseline here: Apollo cost about $107 billion in today's dollars. Here are the yearly figures in that-year-dollars from Wikipedia:

The NASA estimates for the space shuttle (which was being costed and developed around the same time Von Braun and Boeing were putting together) was 43 billion in 2011 dollars. This was based on 50 launches per year, which was very unrealistic (lots more to be said here, effectively NASA planned for the Space Shuttle as being the sole launch vehicle for the entirety of the US including commercial and military launches). The actual final total for the space shuttle was 196 billion, so the estimates were way off. 
Back to the plans. Von Braun updated his plan throughout the Apollo program, and at the very end of his career, proposed his 1969 plan.  This plan was huge, and would likely have required an amount of investment in excess of what Apollo ran (his estimate was a peak of $8 billion per year, which is more than double what Apollo cost at its peak). The first step of the plan was the space shuttle, albeit a far different shuttle than the one you and I know, mainly because it would use a nuclear rocket for propulsion. This would be followed by an earth space station, and finally the creation of the spacecraft which would take us to Mars. The main lifting vehicle from Earth for this would be a future-state Saturn V, the Saturn V -25U. This rocket would be a longer version of the Saturn V which took us to the moon, with four solid rocket boosters attached to the bottom, and the upper stages replaced by NERVA, a nuclear rocket engine. This rocket was entirely technically possible at the time, and would have required significant but not impossible engineering and integration work.
 http://www.astronautix.com/v/vonbraunmarpedition-1969.html
The two Mars ships would be assembled in Earth orbit, fly to Mars using a standard trajectory, astronauts would descend using a to-be-designed descent module, stay for 90 days, then swing by Venus on their way back to Earth, docking with the space station and then returning in the reusable shuttle.
The big driver for the 1969 plan, as well as for a competing plan from Boeing, was the NERVA rocket. Nuclear Engine for Rocket Vehicle Application (NERVA) was a nuclear-based rocket engine. 
 https://en.wikipedia.org/wiki/NERVA#/media/File:NERVA.jpg
This rocket engine was (and may still eventually be) the key to interplanetary travel. In a nuclear rocket, you don't need a chemical fuel. Liquid hydrogen is used, and is heated to a very high temperature in a nuclear reactor. As in a conventional rocket engine, the gas then expands and is propelled out the back of the ship. NERVA would have provided basically twice the fuel efficiency of a chemical rocket. I keep saying 'would have', but NERVA was an extensively developed project. Research on nuclear thermal rockets began in 1952, and continued for two decades. Two engines were built and tested. The second, NERVA XE, was basically a complete flight system and tested in a near-vacuum environment. It ran for a total of 115 minutes and was started 28 separate times. 
 
In my opinion (and the opinion of 1960s engineers far far smarter than I), the answer to whether we could have done it technically is yes. The budget would have needed to exceed that of peak apollo, but that would have included far more than just the Mars mission, but also an earth-orbit space station, a reusable shuttle, and a nuclear rocket engine. Whether those estimates were reasonable, given the massive expansion of the space shuttle compared to initial estimates, is debatable. Whether it would have survived the political pressures not only to cut spending in the 70s and 80s, but also the environmental movement which was (and is) diametrically opposed to nuclear rockets is another. But if we'd been willing to double the investment we were making in Apollo, and public support had existed, I absolutely think we could have gotten not only there but to even more distant parts of our solar system.

A:

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

A:

Probably yes. To add to the other already excellent answers: There is the very relevant blog Spaceflight History which focusses on "space exploration history told through missions & programs that didn't happen".
It has many postings regarding Mars.
Some examples:

The NERVA-Electric Piloted Mars Mission from 1966, which was the last great plan by Braun and would put humans on Mars in 23 September 1986. That might be what you are looking for: it's the most realistic plan from 1966, i.e. when Apollo was not yet doomed.
After EMPIRE: Using Apollo Technology to Explore Mars and Venus from 1965, which would lead to a manned flyby in 1978. Certainly possible.
A New Step in Spaceflight Evolution: To Mars by Flyby-Landing Excursion Mode from 1966, which describes a manned flyby with an orbiter in 1978. Also quite possible and didn't even need peek Apollo.
Humans on Mars in 1995 from 1980-1981, which uses the Shuttle and puts humans on Mars in 1995. This is a realistic plan from 1980 with European involvement.
And if you really want to dream: Dyna-Soar's Martian Cousin from 1960 which uses a version of X-20 Dyna-Soar to put humans on Mars in 1971. But that's more SF as you need a working X-20 in 1965.

