In my opinion, the largest obstacle for such an arsenal would be the large amount of weapons grade nuclear material needed. Where would Israel get it? There is no way they could produce that much in so short a time, and I find it hard to believe that the U.S. would send over that much of it to them.
The second obstacle is quite simpler - what would the delivery vehicles be for the weapons? The amount of targets reachable by the Israeli airforce is not that high - certainly nowhere NEAR 400. Are they putting 50 warheads on each of their three deisel subs? Doubt it. Unless Israel has somehow developed ICBMs, and also has "world power" aspirations", the 400 number seems ridiculous.