"When NASA committed to build New Horizons, it committed to operate the spacecraft and support its science team through its primary mission goal: the Pluto encounter. NASA’s budget projections reflect this (page PS-32 in their 2016 Request, for example). You can see NASA requesting about $20 million per year for New Horizons until 2018, at which point the requests promptly drop to $0.
This isn’t as scary as it looks. It merely reflects that, on paper, the New Horizons mission is only approved through the Pluto encounter, the time it takes to downlink all of the data, and the time it would take to close out the mission. Continued funding is approved every two years based on scientific proposals submitted to NASA and evaluated by an independent review panel. These are called extended missions, and nearly every science mission gets one, owing to the fact that not scuttling a spacecraft actively returning great science to save 0.01% of your budget is a stupidly easy case to make (for the most part).
So while the New Horizons team must make a scientifically sound argument for extended mission funding, it won’t be too hard to do. New Horizons was submitted to a NASA proposal for a “Pluto Kuiper Belt Mission.” The first planetary science Decadal Survey (which prioritizes the scientific goals in the solar system for the decade New Horizons was launched) recommended a mission to Pluto and the Kuiper Belt. New Horizons itself is over-engineered for Pluto (just like Voyager was over-engineered for Jupiter and Saturn). The capability to reach and study a Kuiper belt object beyond Pluto is built in to this mission, and it would be a highly embarrassing and unlikely misstep for NASA to deny a mission extension, particularly a few months after its greatest public outreach moment since the landing of the Curiosity rover."