At what age is a child capable of manipulating his parents/being spoiled?

My husband and I are had a "heated discussion" about this a little while ago. Our 11 week old baby is getting fussier and more demanding and my husband thinks it's because I try my hardest to keep him calm and soothed at all times. He could be labeled a "high needs baby" or a fussy baby. I think it's because of his personality and I should do everything in my power to calm him. Tonight, my husband put him in his crib and wouldn't let me pick him up while he was crying. My husband tried to convince me he was giving me a break, but I was sitting on the couch crying. Our son is mentally and emotionally exhausting, yes, but I don't want to escalate the problem by ignoring his needs. Our baby is a joy to be around when he's fully awake and laughing, but if he gets only the tiniest bit tired-well, it's like Dr. Jekyll and Mr. Hyde. I only let him stay awake about an hour to hour and a half at a time, beyond that, he's inconsolable. My husband says I'm hurting myself emotionally and mentally for the sake of our son, and that I need to let him do more, but I'm the only one who can calm him. I thought at 11 weeks, we are supposed to do everything we can to calm a crying baby. If our son cries for more than a minute, he's screaming. It's not colic, he doesn't fit the criteria in my mind, and there isn't any health issues to be concerned about (that I know of-he doesn't seem to be teething or in pain), it's that he's getting harder and harder to sleep and console. Sorry for the ramblyness, I'm still upset about this.