The super clean tone? It sounds like guitar direct into a higher wattage tweed Fender, or a Silvertone. Or an Ampeg. Just with some extra reverb on it.
Side note: I saw them live about 2 years ago (wearing a shirt I got from that show, today actually). Wennerstrom uses a Vox and goes direct, maybe with a boost and a fuzz on her board, and the lead player was playing something boutique if I remember right.