It has taken me a lot of years sacrificing and saving more than you would believe from my income each month.
You may find that you can get enough of a down payment if you cut out luxuries. You do not need soda, coffee, movies, pay tv service, internet, a brand new car, or all kind of other things that make life more pleasant. Over time you can save a lot. If you did magically get a down payment in your hands now how would you afford it when you have a $4k expense come up?
Buying a house, that may be easy. Keeping that same house, that can be problematic if any financial surprises come along and you are already financially tight.