It is so bad for you -- SO bad. Just because it has been approved by the FDA does not mean it's safe. Drugs deemed safe kill people all the time and get pulled from the market.
I won't bore you with all the details, but maybe do a little research into how it got approved in the first place.
The chemical composition of aspartame is very similar to that of formaldehyde. When it is heated, the chemicals break down and turn into something nearly identical to formaldehyde. Your body is near 100 degrees internally, enough to cause this chemical change.
There are many other issues I could bring up, but suffice it to say that I personally know someone who had a child with severe physical abnormalities due to excess aspartame consumption during pregnancy. Of course you would not be drinking Diet Coke the way she did (all day, every day), but when her doctor sent her to genetic counseling to see if the problem was a fluke or genetic (the baby's brain developed outside of the skull and lived for an hour after the delivery), the genetecist easily pinpointed the aspartame consumption.
I'm not trying to be a fear monger. With most things in pregnancy I am quite laid back. If you asked if it would be OK to drink regular Coke, I would say, "Fine, in moderation." Alcohol? "Fine in moderation." Unpasteurized cheese? "Fine in moderation." But this is one of those things I have done a TON of research on, written several academic papers on, and feel quite strongly about.