The fan needs to be an impeller type and not squirrel cage. Even a ~250W furnace blower (which are squirrel cage) don't do anything for static pressure (DAMHIKT).
I used to think that. A few years ago I hooked up a 100mm centrifugal fan to a high speed mini drill motor and passed the outflow through an 8mm orifice. We were levitating ping pong balls a good few feet above it. And the noise wasn't all that bad.
To your question on CFM for a refrigerator compressor it looks like they're in the 1 CFM (28 liter/minute) range and capable of ~100 PSI. Surprising number of examples of "homemade air compressors" on Youtube using these pumps. They are oil piston compressors just like typical large compressors so I suppose it does make sense.
I don't think 1 cfm will be enough. But if it was then you'd want to build a buffer tank to smooth out the oscillations. And if you're going to do that, then just buy a cheap 2hp compressor.
BTW, even these 2.4 W fans can pump 9.5 cfm with a static pressure of 6.5 inch-aqua. And only produce 32dBA.http://www.jaycar.com.au/productView.asp?ID=YX2530