A proposed architecture for a mission to the Martian moons Phobos and Deimos, with a possible launch date of 2021.
This concept, from the Saskasawa International Center for Space Architecture at the University of Houston, requires the development of a nuclear thermal rocket, which would be difficult (perhaps impossible) under the current political climate.
Even if the political problem could be solved, it’s unlikely that anyone would commit to using such a rocket for a manned mission without at least one long-term in-space test. These factors (and the lack of NASA funding for true deep-space hardware) make the proposed 2021 launch date highly unlikely. The basic concept, however, does appear to be technically sound.
If this is viewed as a one-shot mission, it could be accomplished with conventional chemical rockets and a few more launches, which would still cost less than nuclear-thermal rocket development.