[avmich]

The problem is not so much building as it is cooling small engines. Scaling works against you here. You can download a good simulating tool for liquid fuel rocket engines - http://www.propulsion-analysis.com/ - it will show how, when you're decreasing engine size and fuel flow it becomes not enough fuel to cool of the engine.

Spike nozzle is particularly problematic around the throat, which has bigger area than for a regular bell-shaped nozzle.

[Gravityloss]

A heat sink engine could work in pulsed operation.

[avmich]

True. However this mode isn't very useful when you need to lift something from Earth - or just to keep it in the air.

[Gravityloss]

You could have a glider. Or a boost-glide vehicle to be more precise.