To answer the question, the nazis probably couldn't have ever really gotten to nukes before the end of the war. They had to put more and more of their money into the army rather than research, their economy was being destroyed by allied bombs every minute, and on top of all that, they practically gave us Einstein.
On my Japanese quote earlier, the show was from before all the absoulute crap they're putting on now like pawn stars and the nostradamus effect and all the stuff like that. (in 2005) And there was evidence to back it up; documents, former scientists (who easily I suppose could be actors), several books published by American researchers, and, a little known fact: the Nazis were shipping uranium in submarines towards the end of the war to the Japanese. Once the war was over, and the allies siezed all the nazi ships at sea, the United States pursued this sub aggressively to make sure they got to it first. Also, the program, if it existed, was very poorly funded compared to all the other programs, and got several lucky breaks to get that close, such as guessing correctly on the best method to create nuclear fission. Now, will all that said, I still don't see Japan ever realistically being able to bomb us, nor do I 100% believe this show, because you're all right; the history channel does tell a load of crap all the time and is only getting worse, but, there is some kind of founded evidence.