There have been some questions (and answers) that talk about using an airplane as part (or all) of the launch to space. There are active designs that use wings as part of the launch or landing configuration.
Getting to "space" while not easy, it is simple enough that college groups have made serious attempts to reach space But getting to height is not the important part, going fast is. Being in orbit is about going fast enough so that as gravity pulls you to earth you keep missing it. Getting the speed is the hard part. If you have wings providing lift, you don't need to spend energy on lift it can mostly go to gaining speed.
In theory if you fly around the Earth in a plane fast enough you are in orbit. As you approach orbital speed, your wings start being used to provide downward force so you can stay in the atmosphere and gain more speed with your air breathing engine. Once you have reached optimal speed, point the plane up and you are in the orbit your speed will support.
The Space Shuttle weighs in around 2,000 tons with fuel, while the Antonov An-225 Mriya wieghs in around 640 tons fully loaded. It seems probable that with the lighter fuel requirements of an air breathing engine, a plane that could carry enough fuel to get to the same orbital speeds as the space shuttle is plausible.
So what is keeping us from reaching orbit in a plane with an air breathing engine?