Update

Seth was wrong.

We drove to Home Depot and they had a lovely big selection of o-rings for us to purchase.

So we bought some, took them home, installed it in both water taps on the kitchen sink just for good measure, and thought our problems were over.

Except that our problems are never over in this house.

Turns out the reason the screw ripped the little o-ring to shreds in the first place is because it is the wrong screw. And it would not fit with our new o-ring.

We were not very happy with the people who did that who knows how many years previous to us having to fix their mistake.

So what we did (I keep saying we like I actually had anything to do with the fixing. My parts include: driving to Home Depot with Seth and chronicling it on our blog. That's it.) is install the o-ring, put the screw on as best we could, and then left it alone. As long as we don't try to turn on the cold water tap (and Seth left the little handle off to make sure we didn't in a moment of forgetfulness) the water doesn't leak out of it. He's going to try and find a replacement screw to maybe fix it better.

Which I suppose is better than replacing our whole sink.

And at least our water is turned on now.

Hooray.