Comment by skykooler

Sending humans would be difficult (technically we have the technology already [see Project Orion], it's just illegal), but it's certainly possible to get a probe out there far faster than New Horizons. Travel speed is mainly determined by the delta-v of the upper stage. New Horizons used a Star-48B solid rocket motor to get to its escape trajectory. However, if the probe were smaller, or the launch vehicle bigger, it could have multiple upper stages, significantly increasing the ultimate speed. It might also be feasible to use an ion engine stage with solar panels and a route that dips down below Venus' orbit to get even more speed without increasing the probe mass significantly. In other words, with a large enough budget, we could easily get a probe to those distances in under a decade with no new technology required.