Generally, emotional stressors will not cause premature labor, they may actually delay labor. Emotional stress can however bring on false labor or Braxton Hicks contractions. When the body is under emotional stress the adrenal glands (suprarenal) secrete epinephrine directly into the bloodstream. Epinephrine is a potent vasoconstrictor, this may prolong the birthing process if the woman is at term.
On the other hand, physical stressors can potentially cause prematurity. Depending on the exact nature of the problem labor may come sooner rather than later. There is a condition called placenta previa, in PP the placenta is not in the correct place to facilitate delivery, the placenta is too low in the abdominal cavity. Physical stressors like smoking during pregnancy may precipitate placenta previa. PP most often occurs at the end of the second trimester, this is certainly premature labor.
Stress is something that all pregnant women go through. There are many changes occurring in the body and it is certainly a stressful time. Stress can cause fatigue, sleeplessness, anxiety, poor appetite, and overeating. Short term stress may not be very harmful but over time they can become harmful to the body if they are not dealt with properly.
The normal stressors of every day life generally do not place a pregnant woman at risk for premature labor. The case is different for severe stress. Severe stress may include death in the family, divorce, loss of a job, etc. Stress related hormones may play a role in premature labor but keep in mind that most women do not deliver prematurely due to stress.
It is very important that women find effective ways to deal with stress. If there are any feelings of being overwhelmed, she should speak with her doctor.
I have attached a link below from the March of Dimes. It is a great article dealing with pregnant women and stress.