What do you think about doing a pot luck for a rehersal dinner/lunch?!
As long as everyone knows you aren't trying to be cheap but must do so as you are a young couple and short on money I think it's fine. And I would think anyone invited to the rehearsal dinner would know you well. So here is an idea to spin it, have everyone bring their prized dish and share their recipe with you. Have your maid of honor organize the dishes being brought and how you would like the recipes, like on an index card or hand written on a sheet of pretty paper that you buy for everyone so that you can always think of your friends and family each time you make their special dish.
Or you could do something inexpensive such as chili and cornbread, spaghetti and french bread, sandwich platters with a potato or macaroni salad, rotisserie chickens and mashed potatoes with some rosemary from the grocery store, taco/fajita bar, BBQ, jambalaya etc. Just do something to make whatever stand out a little instead of being the regular, expected food. You could do a late afternoon rehearsal and then just serve snacks and a non-alcoholic punch, which might be less expensive.
If it's lunch, I would do a salad/finger sandwich theme. Keep it simple and elegant. Ask people to make things like chicken salad sandwiches, cheese sandwiches, spinach salad with strawberries, pasta salad, etc.
If it's dinner, I would do a mexican theme. It's always easy... ask people to bring rice, beans, a salad, and then go to a restaurant and order a couple pans of fajitas with the tortillas and salsa. it won't cost too much for just the entree.
Tacky. The rehearsal dinners purpose is to thank the people for coming to the rehearsal. Requesting them to make something is improper. A rehearsal dinner does not have to be fancy though! I had my rehearsal outdoors and I followed it with a BBQ.