It depends, if you have a website that looks for Americans, com,net,org or us tld do not matter.
However, a us domain in a foreign language may confuse search engines and give you the wrong result, that is by considering american a website that isn't, particularly if British, Australian and so on, and therefore pushing it higher on the wrong database, US instead of UK, for instance.
Of course, as stated above, incoming links and link building strategies play a big role.
That's my impression and experience...
Good luck!