Dustin, I've got Parallels 6 running on my 2011 Mac mini w/ OSX 10.7.1 (see sig for specs) without any trouble whatsoever. Runs without any beachballs or hang ups. Even full screen on dual monitors is running perfectly. Parallels has Win XP sp3 installed (all latest MS updates and Parallels drivers).
Try deleting Parallels and redownload the most recent Parallels 6 installer app.
As a caveat I will mention that I am not using a virtual machine from an older version of Parallels. The XP virtual machine is a fresh install from an XP sp2 .iso image. Reason being is that I simply didn't have with me an a copy of a VM to use - the Mac mini is at the office - so I just created a new VM.
Thanks Doc, I appreciate your taking a loot for me. After some more digging, it turns out I had a failing logic board in this system. Apple was kind enough to replace it for me. I reinstalled Lion and restored from my Time Machine backups and Parallels is working perfectly now.
Thats an annoying problem, eh? Fortunately my local Apple store isn't too far of a drive and they fixed it overnight which I appreciate. Lord knows I've spent enough money with them to occasionally ask nicely for a favor.
I take it you are a radiologist from your username? My wife is a lowly x-ray tech and has many times come home with a story to tell about one of your peers. The stories have been good enough she's told me more than once that if my entrepreneurial spirit fails me I should go back to school for something in the medical field.