Not technically the US, but the Confederacy did experience hyperinflation during the war. They ran the printing presses at full-tilt without anything tangible to back them up. And obviously once the tide of the war shifted things got real bad.
Also not technically the U.S, but during the Revolutionary War the continental dollar underwent hyperinflation, leading to the phrase "not worth a continental". By the end of the war they were worth less than 1% of face value and had ceased to circulate as money.