It just depends on the baby. I'm completely sure of when my baby was conceived, and he was born at 35 weeks 0 days and was basically fine. He weighed 6 lb 9 oz. He did have a bit of indrawing when he breathed (meaning his chest caved in as he inhaled), and keeping him warm was a HUGE undertaking, but he didn't go to the NICU at all. He went to the regular newborn nursery for observation after he was born to be hooked up to monitors, and he spent his first night in there because he needed someone who was awake to be watching him. But we went home together on the 3rd day, which is standard at that hospital for vaginal births.
BTW, most doctors agree that when a mom goes into labor on her own early without having a history of premature labor with that pregnancy, it's usually a very happy ending. It's when the baby has to be induced early or when the mom has been having contractions since early in her pregnancy that problems are more common.