So I'm guessing it's either Wynona's Big Brown Beaver or My Name is Mud that you've heard. I'm not really a fan of anything after Pork Soda so that Beaver song is out for me.
I'd suggest listening to the album Sailing the Seas of Cheese and giving it one fair shot. The vocals are different and they do have a pretty unique sound, but there are some real bangers on that album (Here Come the Bastards, American Life, Eleven, Those Damned Blue Collar Tweekers).