That was partially true decades ago, but not valid in modern times at all.
General Motors, the largest producers of cars in the world, has a mere $16 Billion market cap. That's less than Nike...heck, that's less than Harley Davidson ($17 Billion).
The U.S. has a $12 Trillion annual economy. If $16 Billion in market cap disappeared completely, the U.S. at large would never even notice. Losing 1/1,000th of our annual GDP wouldn't even impact a single year of our growth, and future years would certainly never feel it.
The auto industry is more than GM. Got to add the 'foreign' marks such as Toyota and count them. There is also the maintenance and operations part of the industry, e.g., the local service station. Not counting the grossly inflated housing market of the moment, the auto industry is a huge percentage of the national wealth. Cars are like second houses, in time spent inside and in monthly payments and gas/oil. We are wealthy, but a third our wealth is sitting in the driveway quietly oozing various fluids onto the pavement.