I have four children, and experienced the same thing with my second, a daughter. At about 32 weeks, my fluid was 6 or 7. They waited a week and then it was 4 or 5, so I was admitted to the hospital at 33 weeks. The doctors wanted to try and get me to 35 weeks because most babies at that gestation do really well.
The first 24 hours they monitored the baby continuously, and also pumped me full of fluids (while I drank tons of water, as usual). My fluid level barely changed, so they took me off the IV and began only monitoring the baby twice a day for an hour at a time. It was scary because they told me that the danger of having low fluid is that the umbilical cord can get compressed, causing the baby to lose oxygen, which can be quite serious.
After a week in the hospital, it was down to a 3, so my doctor gave me three choices: c-section that day, begin an induction that day, or wait about 5 more days (to get to 35 weeks) and then have the choice of c-section or induction. She did caution me that the baby is at risk and that if the baby got distressed, I would need an emergency c-section. The NICU doctor also came and spoke to me about what to expect. He said by 34 weeks, many babies do quite well, though the most common difficulties are with breathing and eating. There's a good chance that they'll have to go to the NICU, but maybe not.
I chose to do the induction (I've had all my children naturally, with no pain meds and wanted to avoid c-section). Even though I was 2-3 cm dilated when they began the induction, they started it really slow so as not to stress the baby. Exactly 24 hours later, my daughter was born (after just one push!). She was 5 pounds, 1 ounce and 18.5 inches long. They didn't tell me until hours later (after I wondered why they hadn't brought her back yet) that her sugar was dangerously low and they had to take her to the NICU immediately and get her on an IV. (She never had trouble eating or breathing.) She spent 4 days in the NICU, which was very hard (I had to wake up throughout the night and pump my breast milk for her), and after much fighting, I got her out. She weighed only 4 pounds, 13 ounces when I brought her home!
She will be 3 years old on March 9, and is a very bright child. As an infant, she reached her milestones on the later side of normal, but still in the normal range. Today, she knows her shapes, colors, numbers, most of her letters and some of the sounds for them....she is quite a precocious talker....the list goes on and on. I do not see any lasting effects from being born at 34 weeks.
I would say that the hardest part of it all was being away from my children. My oldest daughter (now 4) was 14 months at the time, and being in the hospital from March 1-11 was very difficult--it was the first time I was ever away from her. Then I had to come home 2 days before my new daughter, which was very painful. I do feel blessed that her stay at the NICU was short, though! However, to be honest, it was harder to bond with my 2nd daughter. I think there was some unconscious resentment about being away from my first child, and not having the birth experience I had dreamed of. I also had some postpartum depression, I believe.
I'm hoping not to scare/worry/upset you, but I just want to be honest about it, since you asked. Physically and mentally, my daughter's wonderful! It was me who had the more challenging time!!!! Thankfully, she's Daddy's little girl. I'm still not as close to her as I am with the others, though that could just be a clash of personalities....
Best wishes to you!!! I hope that all goes well, and that you and baby recover quickly. Let us know!!!!