To find a position in USA, no one cares which institute you are from.
Instead, your publication and your technique background should be taken more into account.
No boss will decide to accept you or to reject you just only by your affiliation. I believe this is a general principle in employing an academic person even in Japan. Nowadays, if someone wantS to apply a position in my research team, I will decide ONLY by his scientific level and background to judge if he is an appropriate guy.