New Horizons couldn't do it, because it took a very fast path to Pluto, less than 10 years and was designed around a flyby mission - is just going too fast to stop easily. The plus side is that - as well as getting there as quickly as possible - that as Max Jones says, it gets to do a flyby of at least one small Kuiper belt object, if the extended mission is approved (as surely it will??)
2004 STUDY FOR AN ORBITER OF PLUTO
However, it is technically possible to orbit Pluto, with current technology and without that much difficulty, if you take a bit longer to get there. Here is a plan for a 900 kg spacecraft (about double the mass of New Horizons) which could orbit Pluto in the 2030s if launched in 2016, with one Jupiter flyby gravity assist on the way. That's including fuel, power systems etc. Payload is 19 kg. And it gets to Pluto in summer 2033, and spirals down from the capture orbit, and uses gravity assists from Charon, to start close up scientific observation by 2034. So that's about 18 years for the flight time.
It has an ion thruster motor, like the Dawn Ceres mission - and it accelerates away from Jupiter after the flyby for half its journey - then it decelerates for the rest of the way in order to arrive in the vicinity of Pluto with a low enough delta v for initial capture at a distance of 1.5 million km (that's around four times the distance to the Moon) see Preliminary design of an advanced mission to Pluto
That's a 2004 study - so it would surely be done differently in detail now - but it is a detailed study and gives an idea of what is possible.
It's too late though to design a spacecraft and fly it on this trajectory starting now see
"According to the Mission Design Center’s trajectory browser maintained by NASA Ames Research Center, there are very favorable launch windows for JGA trajectories for a Pluto flyby mission late this year and again late next year. Obviously, this is insufficient time to mount a new mission."
What about the next Pluto mission?
WHEN IS THE EARLIEST WE COULD GET A DEDICATED ORBITER TO PLUTO IF WE STARTED ON THE PROJECT NOW?
Here is a list of possible Pluto trajectories - launch dates 26th November 2015, 14th December 2016 or 31st December 2028 - this is for a flyby, takes around 10 years, so for an orbiter, a few years more
Trajectory Browser
So seems first time we could do an orbiter now - short of a crash program to somehow get an orbiter together by December 2016, if that is even possible - would get it to the planet some time in the early 2040s. At least if we use a Jupiter gravity assist, as New Horizons did.
There may be opportunities to get there sooner using flybys of Venus and Earth that don't need a Jupiter gravity assist that could be launched in the early 2020s - this possibility is mentioned in What about the next Pluto mission?
The original New Horizons mission also looked into a number of other options including Earth gravity assists - where you use the Oberth effect, apply delta v during close flyby of Earth which multiplies the effect of the delta v often by a significant factor.
So - presumably a detailed study would look into those as well, taking into account new capabilities. For more about these ideas, see Draft Environmental Impact Statement for New Horizons Mission (scroll down to 2.3.2 Alternative Trajectories on that page)
The other possibility of course is that with new technology, we find a way to launch spacecraft with much higher delta v from Earth, or a way to get there more quickly.
WHY NEW HORIZONS COULDN'T DO IT, MORE DETAIL
As for the idea of New Horizons doing it if you gave it more fuel - well it had delta v of 13.78 km / sec relative to Pluto when it did the flyby.
So with Pluto escape velocity of 1.3 km / sec it would need to shed 12.5 km / sec. The Oberth effect (where a thrust is more effective if applied deep within a gravity well) doesn't help significantly because Pluto's gravity and escape velocity is so low.
So, that makes it easy to calculate the fuel it would have needed to slow down to get into orbit.
It had a total post launch delta-v of over 290 m/s (1,000 km/h; 650 mph) provided by a 77 kg (170 lb) internal tank
(details from the wikipedia article on New Horizons, and checking up on this info, see also New Horizons for the details of the 77 kg fuel tank and NASA - NSSDC - Spacecraft - Details for the 290 m/s)
So given that we want 12.5 km / s instead of 0.29 km/s for the total delta v - we need to use a lot of fuel to slow it down. To do this properly we’d need to use the rocket equation and feed in the mass of the rocket, specific impulse etc. But we don’t need to do that, to see that it is unfeasible.
The amount of fuel needed to slow down into orbit is going to be at least 77*12.5/0.29 = 3319 kg of fuel.
So, that's not taking account of the need of extra fuel to decelerate the fuel itself + its fuel tank during the maneuver.
Given that New Horizons itself is less than half a ton, obviously it wasn't practical to add more than three tons of extra fuel to try to slow it down at Pluto. You need 77% as much delta v to decelerate to orbit around Pluto as was needed for its record breaking 16.26 escape delta v when launched from Earth.
WHAT ABOUT NEW HORIZONS LAUNCHING A SMALLER "DAUGHTER SPACECRAFT"?
It wouldn't work to launch a smaller "daughter spacecraft" like Beagle II or Huyguens to study Pluto because New Horizons wouldn't be hanging around to relay its signals back to Earth. A daughter satellite could relay signals during the flyby itself - but would soon be out of communication distance with the parent. The whole thing would need to decelerate - power source, radio antenna to communicate with Earth etc.
So that idea was obviously impractical.
They had the choice to get there fast - or to get there more slowly and orbit - but it would seem - not both. At least, not with the technology available at time of launch.
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