Americans have a great can-do attitude and are lucky to have some of the wealthiest land in the world. These two things let them exploit their smarts very well. But bighearted? Not really. Domestic charity doesn't really stand out from the pack and foreign aid is a lesser proportion of GDP than their contemporaries. Their foreign aid is more effective than elsewhere because of the size of their economy, but as a proportion of what is earned, it's not competitive.

My personal experience in the US is that the people are very welcoming and friendly, which leads me to think that Americans are bighearted to people they personally know, but not so much to strangers - eg witness the powerful currents of public opinion against welfare or universal healthcare that don't really exist in contemporary countries.