OK, what's about to break?

[DavieGravy]

Tonight, I noticed that my steering wheel would slowly jiggle from side to side upon application of the gas peddle, as if the tire balance was waaaaay off. It was so bad that it would actually shake my entire arm even at slow speeds like 10 mph. It only did this while I pressed the gas peddle. When I let my foot off the gas, the side to side motion went away. The ailment got worse and worse on my way back from work. After stopping off at the grocery store and driving away, the problem was completely gone. What could cause this intermittent problem? It wasn't raining or snowing, so there was no ice build up on the rims.

Thanks