I have something of a stake in this question because I contributed research to a forthcoming book on this topic, but I would argue that Zionism, and by extension Israel, are not influential in the United States because of the power of the Pro-Israel lobby, it's that the Pro-Israel lobby is powerful because Zionism and Israel are popular.

Moreover, it's the popularity for Zionist causes among gentiles in the US that is really the deciding factor. Prior to the Balfour declaration American Jews were not entirely sold on the Zionist project. Support was strongest among the Eastern European Jews and contrasted with the German Jews. The latter, Jewish anti-Zionist camp used phrases like "America is our Zion" to describe their views.

The Balfour declaration changed that substantially among the Jewish population, but gentile support for the creation of a Jewish state in Palestine in the US can arguably be said to pre-date the Jewish Zionist movement. The Puritans, for instance, explicitly identified their story and struggle with the Jewish search for a homeland. In 1890 an American pastor gathered the signatures of the most prominent gentile businessmen and political leaders in the "Blackstone Memorial" document in support of the restoration of the Jews to the Holy Land.

Since that time this "lobby" has obviously been formalized with the founding of AIPAC in 1963, but there was no AIPAC pressuring Truman, for instance, to recognize Israel 11 minutes after its creation. And actually, without getting into 20 year rule stuff, AIPAC's ability to influence events I think can be overstated, which has been the source of most of the criticism of the Walt/Mearsheimer Israel Lobby book.

Sourcewise, or at least further reading:

See this article by Walter Russell Mead and look for his book in the near future: http://jmhinternational.com/news/news/selectednews/files/2008/08/20080830_ForeignAffairs_TheNewIsraelAndTheOld.pdf

On Jewish Zionism in the US, and indeed Jews in the US altogether, as far as I'm aware the definitive work on this is The Columbia History of Jews and Judaism in America.

There are also some interesting primary source materials during the hearings in Congress on whether or not to back the Balfour declaration. I don't have them at hand, but those resolutions were passed in 1922 and the relevant texts would be the records of the house and senate foreign relations committee for that year.