This app was mentioned in 6 comments, with an average of 1.83 upvotes
WatchMaker has a live wallpaper app and thousands of watch faces that can be used with it from Facerepo.com plus you can make your own, obviously. It's not a widget, clearly, and I don't think it allows you to rotate the watchface every day automatically though.
https://play.google.com/store/apps/details?id=slide.watchFrenzy.lwp
Actually, it turns out Watchmaker does have an app that turns watch faces into Live Wallpaper.
It doesn't respond to taps when used as a lock screen, and when used as a home screen wallpaper, it appears on all screens (so things can look pretty busy when it's covered by icons, which get preference when tapping). I'd find it more useful if they had a widget version.
Depends on the phone you have. If you want something like what I have on my watch on your phone and you have Android you can download https://play.google.com/store/apps/details?id=slide.watchFrenzy.lwp&hl=en
This allows you to set Watch Faces as a live wallpaper.
You can download Watchmaker Live Wallpaper which you can use watch files with apparently. https://play.google.com/store/apps/details?id=slide.watchFrenzy.lwp
I use this to use the same face I'm using on Watchmaker to be my live wallpaper.
https://play.google.com/store/apps/details?id=slide.watchFrenzy.lwp
There is a paid app that will allow you to do that with Watchfaces Here