Does the low population density in America give the wrong impression of resources not being finite?

Interesting question, to which I would answer Yes, in two specific senses:

1) A relatively low, and historically UNEVENLY dispersed population, meant that for a long time, people in America had the correct impression that there was a shifting but always available section of the country that was relatively empty, e.g. with abundant resources. Interestingly, the officially declared "end" of the "frontier" (in the sense of an easily identifiable demarcation between "settled" and "unsettled" lands), in 1890, was soon followed by the first really serious efforts at conservation during the Progressive Era in the USA.

2) Abundance resources, not just of forest and arable land, but of diverse animal and plant species, minerals, water, inland waterways, oceanic ports, etc, etc, has enabled -with a few hiccups- centuries of sustained exponential economic growth in America, which leads some to conclude that any limits must perforce ALWAYS, or at least mostly, be overcomeable somehow. Malthus himself cited America as an example of how fast populations could grow that were not subject to "checks."

However, I doubt whether such thoughts occur CONSCIOUSLY to most people, in America, or around the world. The mother in Bangladesh might more readily appreciate that firewood is scarce, but will that cause her to pause before burning up the last remnant she can scrounge together, in order to have fuel to cook dinner that evening for her family?

Where did you get the idea we have low population density? I think you are wrong. Visit Newark, NJ for a few days.