The United States tried to convince Israel to join the Non Proliferation Treaty (NPT) when the treaty was first introduced and before it was widely believed that Israel had nuclear weapons. The NPT's objective is to prevent the spread of nuclear weapons and weapons technology and further the goal of universal disarmament.
The United States entreated Israel to join the treaty in 1968 and threatened to withhold the sale of advanced U.S. fighter jets if Israel refused. This effort failed because the government of Israel at the time saw nuclear weapons as essential to providing for Israel's security—giving them up would be worse than losing some support from the United States. To this day, Israel maintains a policy of "opacity" regarding its nuclear weapons and has never formally acknowledged them.
Pressuring Israel to join the NPT is still unlikely to work, and the costs of such pressure would probably exceed any indirect benefits. There is no sign that the present government of Israel holds a different view from that of the 1968 government, and if anything, Israel is now less dependent on U.S. support for its security than it was then.
Even so, the appearance of a more impartial or inclusive U.S. non-proliferation policy might lead to increased international support for U.S. pressure on Iran to abandon its more suspicious nuclear activities. But this effort already has strong and growing international support, and a political row between the United States and Israel might undermine their reported cooperation in gathering intelligence on Iran's nuclear program and potentially sabotaging it (for example, with the Stuxnet computer worm that may have slowed Iran's efforts to enrich uranium). The possible "PR" benefit of a U.S. push for Israel to join the NPT is thus unlikely to exceed the costs.