American Administrations actually strongly opposed to Israel going nuclear. In his book "My Promised Land" Ari Shavit writes:

President John F. Kennedy was committed to the nonproliferation of nuclear weapons and was staunchly opposed to the production of nuclear weapons in Dimona. According to an agreement signed between Israel and the United States, American inspection teams were allowed to visit the desert reactor once a year, beginning in 1962.

The Israel's Dimona reactor was built with the help of France, initially, but when Charles de Gaulle became president in 1958, he opposed that cooperation and it was terminated shortly after.

From that time onward, Israel's nuclear capability (including A- and H-bombs) was entirely Israel's own accomplishment. Not only USA never passed any nuclear weapons to Israel, they strictly embargoed any exports that could be used or associated with Israel's nuclear program in any way.

The book I mentioned above is quite an interesting read, and not only on the topic of nuclear weapons.