Stratasys is the manufacturer of most (all?) commercial FDM machines, and they have a print service called Redeye. I toured their facility a couple weeks ago - they have several hundred FDM machines there just for printing on demand, and offer fast turnaround.
Quickparts also offers FDM, and they recently released a Sketchup plugin to upload and get quotes right from inside Sketchup.
I've never ordered from either company, as they're typically ~2-10x the cost of ordering SLS from Shapeways, but have had contact with both and would feel comfortable using them if I needed fast turnaround time. The downside to Shapeways is you may have to wait an extra week for your parts, but that depends on your needs.
Out of curiosity, why do you need FDM? Do you know about other 3D print methods like SLS? They each have their place, so just want to ensure you know all the options. 