"make do" is short for "make ____ do well enough." Make do essentially means "to be able to make something work with what is available."
In the case of your example sentence: "It's a small house, but you'll have to make use of it the best you can" would be a similar sentence with the same meaning.
Other examples:
"Well, all I have to fix the chair is some tape, but I'll have to make do."
"I might not have a lot of income, but I make do in order to support my family."
Hope this helps :)