The only data on the effects of vegan diets is from a few small studies done at a place in Tennessee called the Farm. Everyone there ate vegan diets, including the pregnant women. The studies found that when you eat a really strict vegan diet, you don't get enough vitamin B12 and you may be low on folate and iron, all of which are found in animal products. Some of the women there became profoundly deficient in these three essential compounds.
The first consequence of these deficiencies would be that you'd become anemic because your body wouldn't be able to make enough red blood cells without those nutrients. If you're anemic, you have a harder time fighting infection, and you may have an increased risk of bleeding after you give birth.
If you're really deficient in vitamin B12, you can develop a neuropathic condition that causes muscle weakness and nerve damage. As for folate, we know that folic acid supplementation before pregnancy and in the first weeks of pregnancy will decrease the incidence of neural tube defects.