First of all, to address the OP’s question, no, it can’t be done with existing hardware, or equipment readily derived from current hardware. As others have noted, the Shuttle can’t even get beyond near earth orbit (see this recent thread), nor do we have the capability to perform a direct ground-to-interplanetary mission for any vessel large enough to serve as a lifesystem for interplanetary travel.
Second, as many have pointed out, creating a closed-system environment capable of sustaining life (with the requisite redunancy) for the 29 months required for a minimum energy Hohmann transfer is beyond what we currently have available. Remember, no lifeboat back home, no Progress supply ships; your system has to be failsafe and redundant. Providing rotation for gravity simulation seems simple, but we’ve never done it with a permenant space habitat; it may seem simple, but even a small instability can cause a catastrophic, unrecoverable problem in interplanetary space, and propulsion would have to account for gyroscopic forces or cancel the spin during navigation maneuvers.
Even more problematic is radiation shielding; while a powerful magnetic field could deflect charged particles emitted by the Sun, such an intense field would require more energy than we could conceivably provide, and as Frylock notes, such a field may have detrimental effects on the crew. (Long term effects of intense magnetic fields is an area not well developed.) This fact is glossed over not just by Zubin but by most proposals for a Mars mission. See this thread for more discussion on the hazards of radiation in space.
The propulsion issue detailed by mr_wired isn’t really a problem; if we can get to a cislunar orbit, it takes very little extra delta-V to achieve an Earth escape orbit. Insertion into Mars orbit is a little more tricky, as you have to carry the additional fuel (or perform some kind of risky aerobraking maneuver with your interplanetary craft), but the delta-V requirements aren’t prohibitive. Ditto for the return flight. However, the extended duration of a free Hohmann trajectory exposes your crew to grave risk from solar flares along with the other hazards of space and microgravity. (The same problem, with regard to flares, existed during the Apollo program but the short mission durations and the ability of mission planning to avoid times of known peak activity minimized the risk. A months-long mission wouldn’t have the same benefit.) It would be much preferable to have some kind of low constant thrust, high specific impulse motor than can use a flatter powered orbit trajectory to reduce that time by a half order of magnitude or better. Although we have some ion/plasma motors in development for low propellent stationkeeping operations for satellites, we don’t have anything in the works that is sufficient to be used for a large craft.
So, not only could we not conceivably do a Mars mission with off-the-shelf equipment, but we lack the experience and technology to do it with any degree of safety and a reasonable chance of success (90%+) at all. At a minimum, we’d need both better environment systems, some way to spin for gravity and protect against radiation, or a higher I[sub]sp[/sub] constant thrust propulsion system, all of which are decades away from man-rated operation. At a mimimum, even with a massive, Apollo-style blank check effort I can’t see it taking less than on close order of two decades to develop and mature the requisite technology.
I won’t even get into the question of why you’d want to send people to Mars when there are far more scientific and resource valuable targets that are much easier to reach.
Stranger