My mom stayed for a full month after my son was born. It was incredible. Yes, there were times that I think my husband felt a little overwhelmed in our small apartment but he also saw how much I needed her to be there and that having her there meant he could go back to work earlier without worrying about me and we wouldn't loose all that income. I had a rough labor and a long recovery so having her there to cook, do laundry, clean, bring me water, hold the baby so I could take a shower, etc. was invaluable. We had a blow up mattress for her in the living room. The way our apartment was set up was that there was no wall between our bedroom and the kitchen so we ended up hanging up a sheet screen around our "bedroom" so we had some semblance of privacy.
My mom is the kind of person who thrives when taking care of people. She was a nurse too. So, she totally knew exactly what I needed when I needed it.
I think that as long as the person who is visiting understands that you and your husband will not be playing host and they are there to help first and foremost then it shouldn't be too bad.