Actually what you are proposing is called a SSTO - Single Stage To Orbit.
If I were to design one (and I have designed countless in a simulator game called Kerbin Space Program - which is pretty realistic to be called a simulator) I would add a set of swept wings, which are best for very high speed and engines with afterburner. The aircraft would then need oxidizer for the place in space where is no oxygen and then some cold thrusters to maneuver the thing in space, without starting the huge engine. In Space the thrust needed would be low.
The idea would be to take off like a plane and reach supersonic speeds in the higher layers of the atmosphere. The aircraft would point a little up and BAM, the afterburner kicks in. This would get the spacecraft outside of the air which slows it down. After the drag is reduced the nose is tilted down so velocity is building. Eventually, if everything is timed just right, you should get there.
Totally possible! But it would still be a spacecraft, not a plane :D
Hmm.
I loved the fact that you detailed all of these information.
It's Great!! Nothing short of that.
Howbeit, this would resemble the Xenu space plane
:)) Ah, the wonder!
I must convert :)