The United States Department of Transportation, Bureau of Transportation Statistics (BTS) reports that there are 272,480,899 vehicles that are registered for for highway use as of 2017. An additional 63,759 mass transit buses are also registered. Given a population estimate of 327,167,434 as of July 1, 2018 of which 22.4% are below the age of 18, that gives a population of about 253,881,929.
That makes the claim to be plausible with about 1.07 registered highway vehicles in the United States per every resident 18 years or older, with a nominal increase if mass transit vehicles are included.