Ah I finally came up with a trick that worked with only moderate tediousness.

Bring up a 1-night weekend reservation listing. Click on each of the 40 hotel names shown and look at the "rates from $X" figure. Go down the list until you find the cheapest one.

Then go back and drill into the calendar and find when those cheap days are open.

In my case it's $59 Friday or Saturday night at Fairfield Rancho Cordova. There's a ton of Marriotts near the Sacramento airport, but they don't get cheap enough on the weekend.

Thanks!