NO!!! You cannot spoil a tiny baby!!! Eek--I don't know why there are still people out there that tell that myth to new moms.
If anyone tells you that you are "spoiling" your baby, tell them that all the latest research shows that babies who are held a lot (especially in the early months) and have their cries responded to promptly actually cry LESS, not more in the long run. This is because they are happy and secure. Babies whose needs haven't been met from early on average tend to be whiny and clingy later as children. There are longterm effects into adulthood as well--adults who were cuddled a lot as kids are much happier! Yes, there are a few babies who do stop crying to be held, but this is because their spirits have been broken and they know not to bother crying because no one will help them.
A happy and secure baby will eventually learn how to soothe him/herself to sleep. Try to get your baby to nap during the day so that he won't be overly tired at night. Establishing a standard bedtime routine will help. We would swaddle our son, rock him until he was drowsy, then put him down. If he started crying, we'd pick him back up and rock him again until he was almost asleep and put him back down. We repeated this until he fell asleep. Eventually we could put him in bed tired but awake and he'd go asleep on his own. Our son had terrible reflux and cried a lot for the first four months. But the is the happiest toddler now, cries less than most, sleeps almost 12 hours a night--and this is after we NEVER let him cry it out.
Check out Askdrsears.com. He has a lot of advice on soothing fussy babies. Also, I like the "Happiest Baby on the Block" DVD because Dr. Karp demonstrates his soothing techniques.
Remember that this fussy phase will pass--even though it probably feels like an eternity right now! Good luck!