Meersheimer published a book, The Israeli Lobby and US Foreign Policy, in 2007. In the last chapter he covers Iran. He writes:
Iran's nuclear ambitions do not pose an existential threat to the US. If Washington could live with a nuclear Soviet Union, a nuclear China or even a nuclear North Korea then it can live with a nuclear Iran.
I think whilst Meersheimer is correct here, there is a great deal to be said for applying political pressure to prevent the proliferation of nuclear arsenals to countries which harbour nuclear ambitions, but do not have them. A little earlier, he writes:
Iran is widely seen as [Israels] most dangerous enemy as it's the adversary most likely to obtain nuclear weapons. Virtually all Israelis regard an Islamic country in the Middle East with nuclear weapons as an existential threat. The Israeli Defence minister, Binyamin Ben-Eliezer remarked one month before the Iraq war "Iraq is a problem ... But you should understand, if you ask me, today Iran is more dangerous than Iraq"
Sharon began publically pushing the US to confront Iran in Nov 2002, in a high profile interview in The Times (London). Describing Iran as the "centre of world terrorism" and bent on acquiring nuclear weapons, he declared that the Bush administration should put a strong arm on Iran "the day after" it conquered Iraq.
In late April 2003, Ha'aretz reported that the Israeli ambassador in Washington was now calling for regime change in Iran. The overthrow of Saddam, he noted, was "not enough". In his words, "America has to follow through. We still have great threats of that magnitude coming from Syria, coming from Iran.
I imagine he no longer views Syria as posing a threat. Meersheimer concludes his book by writing:
It is not surprising that Israel & it's American supporters want the US to deal with any and all threats to the security of Israel. If their efforts to shape US policy succeed, then Israels enemies get weakened or overthrown, Israel gets a free hand with the Palestinians, and the US does most of the fighting, dying, rebuilding & paying.
He asks the question: "can the Lobby's power be curtailed?" And answers this by saying:
this is not going to happen any time soon. AIPAC and it's allies (including Christian Zionists) have no serious opponents in the lobbying world. They know it had become more difficult today to make Israels case and they have responded by expanding their activities and their staff ... [moreover], major media outlets will remain sympathetic towards Israel no matter what it does.