Sway Bar Links? Motor Mounts? I'm dumbfounded.

Hey guys, I recently bought a 2003 Tacoma, I am absolutely in love with it so far! The day after I bought it I started noticing a bit of a "shift" (almost feels like a bad motor mount) when I had to come to an abrupt stop and since then it's been happening every time I come to a stop. I know from the pre-purchase inspection that one of the sway bar end links is busted, and I intend on fixing it as soon as I can. My questions are, could the shift be caused by a broken sway bar link? Or should I be looking more in the direction of a motor mount problem? And with either of these, is there any serious damage I could be causing, or worsening, by driving it?

 

First, fix that broken link (or remove the entire sway bar as some folks do) and see if that solves it. If not, then look further.