Can't spoil a newborn?

Ok, we've all heard that you can't spoil a baby in the first 3 months so just give them whatever they want. I have taken full advantage of that and have LOVED the excuse to cuddle my son endlessly. However, he's 10 weeks old now and it seems like he can't/won't sleep unless I'm holding him or laying down next to him. I let him sleep next to me at night from the beginning and often laid down with him for naps, especially his one longer one each early afternoon that overlaps with my 3-year old's nap. How do I work to break him of needing me next to him? Ex: he was just sleeping peacefully during his long afternoon nap and about 30 seconds after I silently slid out of bed, he started squeaking and is waking up. What do I do? I can't always sleep next to him - I need to start getting stuff done during his sleep times! Not to mention he needs to start transitioning out of my bed at night. Help!