The basis for the evangelical's support of Israel is it's interpretation of "bible prophecy" which interpretation teaches that Israel is back in Palestine in fulfilment of the bible's prophecies about it.
Some of the groups that would hold that tenet would be most of the Pentecostal and Baptist groupings, including the powerful Southern Baptist Union also you would have many independents. The number is upward of about 20 million (the population of Aussie) and despite other differences they would all converge on this teaching about Israel and the land of Palestine.
As far as the Evangelical Lutherans go they are a relatively small denomination that had it's roots in the reformation. Luther in fact was strongly anti-Jewish as was the Catholic Church to which he once belonged.
The reformers generally taught that the Christian Church replaced national Israel and all the promises in the bible about the land etc.are to be taken in a spiritual sense. eg, Jerusalem is heaven and Israel is the church etc. There are other evangelicals in the US who hold this view also but are very much in the minority.
On the other hand the major groupings that are generally covered under the term evangelical, have a bible interpretation which has parts of the bible that belong specifically to the Jewish people (eg. promises about the return of the Jewish people to Palestine) and others that belong to the Christian Church. That is a very pervasive teaching in that broad grouping and with some, acceptance of that interpretation is even a test of orthodoxy.
(As an aside it helps give an insight into why the US supports Israel so strongly. We're talking about a religious culture which is a numerically significant part of the Nation. Also I would suggest that that support spills over into the wider US community even, though it may not be able to articulate that support in religious terms).
