Any tsunami one of the Great Lakes, might not be so mini. It would depend on the type of event that caused it. If a big meteorite/small asteroid hit Lake Michigan, Chicago would cease to exist. The same would be true for an (unlikely) major earthquake under the Lakes. It might even flood the Mississippi river, since it's tributaries come pretty close to the lake, and the tsunami could wash out the high ground, such as it is, between the Lake and the tributaries of the Mississippi. There's even a canal, that connects Lake Michigan to the Des Plaines River, a tributary of the Mississippi. I once read that during WW-II submarines were built on the Lakes, at Manitowoc, Wisconsin, and then sent down the Mississippi via the canal, on floating dry docks, which the boats met at Lockport, IL.
I'll take this guy's word.
"Tsunamis are born along the borders of the Earth's tectonic plates, where earthquakes and volcanoes are common. Because the Great Lakes are not situated near the edge of a tectonic plate, tsunamis cannot happen here, said Peter Wampler, assistant geology professor at Grand Valley State University."