I'd say the best bet for such a brand here is Cunningham. They were effectively carrying the American flag at Le Mans in the 1950s and doing it almost singlehandedly, and the cars of the 1950s were fast.
Cadillac became an Arm of GM very early on, so unless GM wants to fund turning Cadillac into an exotic manufacturer, I doubt that one will go anywhere. Cadillac is getting a mojo now because GM knows that relying on older customers for Cadillac will send them into extinction, and they instead decided to go after BMW, and are doing it shockingly well. Duesenberg is an interesting idea, but they were less into GTs and more into big luxury sedans, so they would likely be more of a rival to Rolls-Royce than to Ferrari or Aston Martin.
If you are willing to do it in later years, you can go with Saleen, Vector or Callaway as well, but these don't show up until the mid-1980s. All three made convincing exotics in the 1990s and 2000s (Callaway C12, Vector W8TT and M12, Saleen S7) but didn't really get considered an American exotic maker. Modern companies can break into that mold - Pagani has done so in the last decade - but its harder now because of the development of such cars being expensive and time consuming.
One other prospect I had in mind was Shadow, the American F1 team that began in the mid-60s. At the time, American companies (Ford in particular) were running roughshod over international motorsport - Ford nailed the quartet of racing triupmhs - Indy 500, F1 World Championship, Le Mans win and WRC champs - all in one year (1968) and some of the designs around at the time were something wicked. I can imagine a Shadow supercar, perhaps using one of the American race engines as a base (or maybe even the Cosworth DFV, for that matter), making for a lightweight, fast car.