Actually physically getting humans and their life support to Mars is likely to be feasible. But there is much more to it than that. 

LANDING SAFELY

First - they have to land there safely. Landing on Mars is far harder than anywhere else in the inner solar system, if you need a soft landing. 

The problem is - that the atmosphere is so thin, it's not enough to slow you down to a soft landing even with huge parachutes. But it is still enough so that as soon as you hit the Mars atmosphere you are totally committed.

Most of us don't give much thought to the idea of escaping our problems on Earth by going into space. But those who want to colonize Mars often see it as an urgent need for humanity, to have a potential "second home" as they see it. It's also a common theme of science fiction, for instance in "If I forget thee, Oh Earth" by Arthur C. Clarke. In this case his young protagonist is on the Moon, looking towards the Earth.

Did our two Viking landers find life on Mars in 1976? Astonishingly, thirty seven years later, we still haven't sent anything to Mars able to answer this question for sure.  None of our spacecraft since Viking would be able to spot life which we now know exists in the driest deserts on Earth, and only one of the experiments on Viking had this capability. There are  hypotheses about what they found, but no definite proof.

A few years back, to everyone's complete surprise, Joseph Miller, specialist in rhythms of life, spotted smooth daily cycles in the data from 1976, strongly suggesting life processes. So did Viking spot life or are these smooth cycles signs of something else, perhaps some complex chemistry?

When astronauts get sick from zero g during long duration flights in zero g, the best medicine is to return them to Earth and full gravity. So, what if they could spend a few hours or minutes a day in artificial gravity during the flight?

It's far easier to do this if humans can tolerate fast spin rates, say as fast as 30 rpm, at least for a short while. Artificial gravity varies as the square of the spin rate, for instance, at 30 rpm you get full g in a centrifuge with a diameter of 2 meters- while at 3 rpm, you need a diameter of 200 meters (nearly three times the size of the ISS).

Joseph Carroll's ingenious idea is to attach a tether from the crewed Soyuz spaceship to its final stage - and use this as a counterweight to do the first ever real experiment in tethered artificial gravity. He has found a way to do this without using a drop of extra fuel.