A marriage should not be built nor revolve on whether or not there is a house. You either want to be married or not. As others have mentioned, closing on a house is a very long and complicated process. It is also very expensive, as there are hidden costs and processessing fees when buying a home...even with a pre-approval.
Realistically, if you don't have at least 6-7 thousand dollars liquid cash in your bank account for the closing cost of the house alone (this is a conservative guess as we don't know what the mortgage is going to be etc. It could be more than this) you will not be able to both have a wedding and buy a house.
If I were you, I'd get married first, then worry about buying a house later if that is ultimately what you want. Even if you were to get approved for this house next week, it could be months before you could move in depending on unforseen factors. Then is this place move-in ready? Do you have the basic necessities for when you move in? And if not, where will the money come from for this? If you have a small wedding, chances are slim that you'll get enough gifts and money to furnish your home with the basics.
Everytime I've moved, I've needed quite a bit money for incidentals, like paper plates, food/dry goods, toiletries, and any furniture or basic items like beds and/or bedding, chairs and a table, cooking utensils, pots, pans, and maybe dishes for the first weeks in your new home before every thing is unpacked. Things like bathroom rugs, towels, cleaning supplies, and curtains/drapes/shades are really important and add up. Don't forget landscaping items such as lawn mower, snowblower, shovels, sprinklers, rakes, trimmers. You will need these right away to keep the property looking good and safe (if it's winter) on the outside, that is, if you don't have a service and if you want to be a good neighbor.
If you plan on having a wedding at the home right away, will it be up and running well enough to host people? Even for a simple cookout? Will you have chairs, seating, shelter if the weather is bad and so on?
I say keep it simple and manageable. Go get married at a chapel or church. Then get the house. Mixing the two is going to be too stressful and in the end complicate things too much financially. If you sit down and do the math, you'll find you'll be better off and further ahead financially going to the Virgin Islands or Vegas for a quick wedding and honeymoon, than doing the down home wedding that is all dependent on whether or not you get a house.
Doing a weekend get away, you'll only have to worry about your license, transportation and one or two nights at a hotel. There are so many cheap wedding packages you could have a nice wedding, cheap and fast (definitely under $1,000). The other way, you have to worry about food, and entertaining, and possibly fixing up the house and/or yard so you can host a party...which adds up fast.
Seriously, I think you two need to go price shopping for everything you'll need in the coming months from filling a house with furniture to downpayments, to utilities, to gas, to medical, wedding costs etc. If necessary go to a finance counselor...someone who understands money and expenses to help you budget. It sounds like your fiance doesn't have business sense. No insult meant. But really he should know this is probably a bad, cart before the horse move if money is tight.
From what you share, I think you both would be better off eloping and then renting an apartment and saving your money up for a couple of years. There is nothing more stressful or a more surefire way to wind up divorced than to burden a marriage from day one with crushing debt.
Remember, if you can't keep the payments up on this house and lose it, you will probably never get into another house again in this current financial climate. Excellent credit is at a premimum, and no one gets second chances where mortgages are concerned anymore.
Furthermore, it sounds like you don't talk to each other about the sort of things that are important for a healthy, productive marriage. There's too much focus on houses and wedding details and not enough talk about finances, and future goals and how to get there.
Besides a finance counselor, find a marriage counselor or pastor for pre-marriage preparation. They too can help you wisely navigate these sorts of concerns and questions and facilitate healthy adult conversations about life goals. This is so important if you want to start your lives off in the right direction. Just remember, because you both WANT something, doesn't mean it is a good thing, or the best thing for you. You two need to talk and now about the reality of what you can and can not have....not spin your wheels about what you WANT.
Good luck.