The US of then is different from the US of now. Now the US roles over, and is more then apt to take the easy way out. Long gone is the influence of those pioneers which sacrificed sweat, blood, tears, limb, and life to create this great nation. However, back then that influence was much stronger in the national character. Remember the ill planned
Mexican Expedition. Therefore, it would be safe to assume that the US wouldn't have sued for peace at anytime.
As for Japan being able to do anything big on the west coast. I don't believe that was possible. Japanese forces and resources were already focused on their main goals, the Dutch East Indies, and foreign posessions which stood in between it and Japan. They would have been unable to conduct amphibious operations of any kind towards the eastern pacific. However, if they did, I believe that the small force which they would have been able to land, even if it had been able to hold ground, would eventually lack the logistical support to mantain their preserce, or to enlarge its presence. Therefore, they would eventually be forced to conduct a fighting retreat to the beaches, or surrender.