I have one of those husbands who says no to everything. I don't know why he bothers because after 20 years of being married to me, he should know me better than that. lol I just realize that when HE says 'no,' that means I can plan on doing it entirely without his help, and that I'll have to get really creative with resourcing and financing. You can cut the feed bill significantly by growing chicken forage (I seem to be especially adept at weed growing), and if you research it carefully to make sure you don't feed them No-no's, you can feed them many of your kitchen scraps. You'd be amazed at what you can gather for free if you spread the word around what you're trying to do and that you're looking for scraps/lumber/supplies etc. Seems like there is always some farmer or hobbyist looking to scale back or get rid of unused stuff, or someone needing to move an old shed or kids' playhouse in order to replace it with a new one...your church, your neighborhood, any clubs you might be associated with, or even go post fliers at a VFW or rotary club etc. Chances are, there is someone/people who work in the local school who has or is raising chickens or some other livestock, who has old spare stuff around you can collect.
I think I collected baby supplies/clothes for 8 years before I acutally ever got pregnant, so when I eventually did, I had most of what I really needed. Even if you can't start your coop now, you could create your "chicken hope chest" of stuff you find at thrift stores, etc. that you plan to use with your birds. Eventually, you'll have so much stuff it won't seem like a big financial hit to get started, OR your circumstanced will have improved enough that you'll be all ready to get the show on the road.

Don't give up. You're as entitled to YOUR hobbies as your husband is to his--especially one that comes with so many perks like chickens do. Hey!...without even knowing it, your husband could be providing you with one ready-made coop wall.

If you build your coop using the outside back wall of his shed as one wall of your coop? Hey, remind him marriage IS compromise, and you're a lot more snuggly than a bandsaw is! lol