I am surprised to hear this story ... I can't imagine him not being able to get a single day off for the birth of his child! You have to weigh two things ... his presence at the birth of his child and his ability to keep his job (and the necessity of that job). Normally, I'd say absolutely he should tell his employer he simply cannot come to work because he cannot miss this once-in-a-lifetime event. If that means he'll be suspended, so be it. Fired? So be it. If, however, you think there's a real possibility of losing his job and not being able to find another given the state of the economy, you need to think long and hard about it. Losing a job these days can have serious consequences. You don't say when he works, but if there's no better solution, do you think you could be induced Friday? If you're induced at noon and he works until 3 he could definitely be there ... or induced in the afternoon and he works until 7. First time moms are usually in labor for 10+ hours (often more for induction -- also, if they're using Cervadil, it induction in a multi-day process). If he needs that job, see if there's a compromise short of risking his job.
Secondly, I wholeheartedly agree that you don't need to wait until you can afford a big wedding. Work on the MARRIAGE -- the wedding is just a chance for the people you love to celebrate your commitment and share in your joy (my parents have been married for nearly 30 years and have the best marriage I know -- their reception was punch and cookies in the basement of the church where they were married. Not fancy, but they were married at the end of the day, so the wedding WORKED!). I'd recommend doing premarital counseling through your church and then gather the few people you love most and go to city hall. If you want, you can always have a party afterward to celebrate with friends (and then it can just be a party instead of being a WEDDING RECEPTION -- which for some reason has to cost 20x more than any other party you'll ever throw). Or have a simple ceremony with a few close friends and relatives and serve punch and dessert around 4 p.m. At the end of the day, you will be married, which is all that matters. Then you can focus on creating a wonderful, warm and Godly home for that baby!