Does stress impair your short term memory? I have noticed frequently, when in a very stressful situation (particularly emotional stress), I will forget things very quickly. To give an example:

Recently, I got in a heated argument with a friend. During the fight, a third friend came in and tried to break it up. "What is this about?" he asked. I was about to answer, and then it occurred to me I didn't know. I was still angry, but the information had already escaped my mind.

I have noticed this happen more than once. I asked someone about it, and they said they had had similar experiences. 

Is there some hard science to support the idea that stress negatively affects short term memory?
It really depends on the timing of the stressful event, as well as anticipation. From an evolutionary standpoint, "stress" developed for a reason in the context of heightened arousal, attention, preparation for action, etc. Say you encounter a lion in your backyard: Not only will your sympathetic nervous system be on full speed, but several cortices are also geared up to processing what's going on. The idea is that you want to make a quick behavioral response, so inducing stress short term actually facilitates many different processes, including encoding of memory. See the link below for some research on this, I grabbed one that should be open access.

http://www.ncbi.nlm.nih.gov/pubmed/22483973

Basically short term, acute stress may help encoding of memory, whereas long term, chronic stress not so much. Also consider whether or not you are learning something and then hear a loud human scream in your ear. This may disrupt encoding. So again, it's the timing that is important. And I would say it depends on the type of stress.