American Armored forces were understandably concerned but knew their limitations, for the most part, and they had a lot of well-founded confidence in their leadership, their tactics, their air power, and their artillery, all four of which which were the great equalizers on the battlefield.
Courage was not lacking. My neighbor, when I was growing up, had been a Sherman tank commander in the 2nd Armored Division (Hell On Wheels) in Europe and had a great respect for, and yes, fear of the heavy German tanks, but he, like thousands of other tankers had a job to do and they did it valiantly. Among other battles, he was involved in the infamous night skirmish near the Falaise Gap where his unit was heavily outnumbered and low on fuel. They dug in and ended up in hand-to-hand combat with the Germans in pitch black conditions after midnight. They managed to hold the line and in the morning, despite an estimated 5:1 disadvantage in tanks and manpower, more than 100 German vehicles had been destroyed, more than 400 enemy soldiers lay dead and around 1,000 prisoners had been taken.
Nobody can claim from an armchair that they would have the courage to do that, but in times of need when it comes down to life or death, it's amazing the courage one can summon in the face of great odds.