Gusto never bit over it (although he would head-whip at my hand once in a while), but he was really, really uncomfortable with the clipping. His nails are mostly white, and pretty soft and thin, and I think the clippers did genuinely pinch and hurt a bit.
The dremel has made such a huge difference. Not only is he much more comfortable, but because I was so paranoid about hitting the quick, I never even tried to get his nails to shorten.
I spent a week or so before I even started trying to dremel doing foot handling without clipping at all, and just overloading him with treats. I wanted to try and break the association between my hands on his feet and clipping. I did it all on my bed, where he's very comfortable (when I dremel, I just throw a big sheet over the top so I don't have nail dust on my bed). Lots of touching = cookie stuff.
Once I got the dremel, he got comfortable with it a lot faster than I thought. We did maybe 2 sessions of touching the nails with it off before I started turning it on very low. I'd run it, turn it off, touch a nail, turn it back on. Eventually worked up to touching the nails by probably the 3rd session. Kept it low for a few times and didn't really work on getting the nails shorter, but within a week, I could turn it up and really go to town.
I didn't even try the back feet for the first couple of weeks, but for whatever reason, he didn't care about them at all when I did start. For some reason I thought they would be harder.
It's all worked really well. I can do each foot with maybe one cookie in the middle (I jump back and forth from toe to toe). I had the sheet down two nights ago, but started with Meg who was also on the bed (and just gets clipped). When I finished her and turned to him, he was sitting near the dremel with a dark drool stain on the sheet. Pavlov would be very pleased.