To further Chris's post, compressorless atmospheric jet engines are actually quite common. There's one in most DIY's tool kit, it's his blow torch.
The blow torch makes pretty minimal thrust for the fuel used. The combustion chamber pressure is limited to about atmospheric, and air is induced only by venturi effect from the high speed fuel jet supplying the burner. Without combustion chamber pressure, there is no exhaust jet thrust. I've measured the thrust from a small torch (bored at work one day). Used a torch lighter. It managed to make about 1/10gram of thrust. Nothing.
Compressorless jet engines also exist in the non-air-breathing set. Oxy-fuel torches all the way to liquid fuel rocket engines. These ARE compressorless jet engines. In liquid fuelled rockets, the combustion chamber pressures are limited only by material limitations and the pressure your fuel/oxy pumps can deliver. Thus, the chamber pressure can be high, and so can the thrust.
Without a method to adequately concentrate the oxidizer, and supply it to the burner at a pressure above chamber pressures, jet engines cannot produce meaningful thrust on a continuous basis. It is possible intermittently, as in the Argus pulsejet (or indeed any pulsejet engine) on the V1 (pulsejets aren't truely compressorless either, actually, as they use tuned pipe resonance to achieve compression acoustically).
Food for thought.
J