I am getting my new digital receiver next week, and I have my speakers set up in a small, 15 X 15 foot bedroom. Will this small space make for a different surround sound effect, than say, a large living room?

Assuming all of the speakers are balanced it shouldn't.

Now having said that certainly a bigger room would allow you to have more sound and longer reverb times.

The closer the surrounds are to the mains the more mixed the sound. I only have about 13' front to back and I had trouble getting mine set up.

Is this a good thing or a bad thing?

Can be a bad thing. Most of the sound from surrounds is supposed to be ambient, the score, background noise etc. It's with the directional sound likes bullets whizzing by or planes flying overhead that speakers too close together will blur the sound and you won't achieve the same effect. When I had my surrounds hung on the wall he suggested putting them behind me instead of to the sides to get them an extra couple feet away from the mains. The good thing is nothing is permanent so before big holes are drilled try them in different places and see what sounds better.

you can balance the surrounds to achieve a convincing surround effect regardless of room size. the main draw back to a small room is achieving reasonably flat, low bass.