A ship idea which was only refused for it would take a couple billion dollars would get us to Mars in three month approximately which a steady amount of speed. It was given to them through the credit of one man when a group had forged the idea. It was well thought out and possible. Gathering the money, time, and people, in about 6-7 years it would be possible. Especially if he had the ship idea in mind.
When Kennedy said we would go to the moon by the end of the decade, people were very skeptical but it happened. The science and the technology that we need to make this happen is within our reach, and Tesla certainly has the skills and the power to make this possible.
Yes, it is feasible to inhabit Mars within the next 6 years because the technology exists. Elon Musk simply needs to recruit enough people who would be willing to be the guinea pigs on the world's first voyage. It will not be difficult to get them there; it will be harder to get a team together.
NASA has been testing an inertia-less drive of the Star Trek variety and is preparing to launch the first test version into space. The physicists have no real clue how it works, much less why, but work it does. Without spitting anything out the back whatsoever, it produces thrust and, theoretically, a nuclear powered version could go to the moon in four hours and Mars in a few weeks.
Six years might be pushing it, but its certainly feasible with this kind of technology.
Elon Musk has some interesting and creative ideas. It does make sense that we need to expand from Earth to elsewhere due to overpopulation and scarcity of resources. However he's currently estimating that it would cost about $10 billion per person to get to Mars, and I just don't see how that's workable.
It will not be possible to inhabit Mars in six years. Explorers would need way too many resources to make the planet livable. It would also be depressing, as so much of Mars surface is an orange-red color rather than green. Humans don't belong on any other planets right now.