Q&A: Help! My newborn wants to be held all the time.

It is truly extraordinary how temperamentally different humans are, from one extreme of life to the other. Some are inherently unflappable and content with their own company, and some need constant attention and soothing. Think of a handful of adults in your life, and how temperamentally diverse they can be.
Your newborn is teaching you through his temperament and behavior how to parent him right now.
A very basic need of the early infant is to develop a trust in his caretakers and the world. A trust that he will be cared for, and that his needs will be met so no, you are not spoiling him by holding him when he seems to need it. A child so young can't be spoiled.
Mothers in many other societies strap their infants on their back, front or side and off they go to get the day's tasks done. Invest in a good 'Snuggly' and give your four-week-old the experience he knows best, that of being close to the sounds and rhythms of another.
Having said that, I need to acknowledge what your husband might be feeling. While your newborn is important, his are not the only needs in your home. If you are busy and your son ends up crying a bit before being tended to, you shouldn't feel guilty. Our children are also born with some resiliance.
As your infant gets older and more adept at looking at, mouthing, then playing with different objects, he will get better at self-entertainment and you will have a few more precious moments to yourself.