In fact they drive most politics all over the world in general, but ESPECIALLY in the US. Pretty much the entire government is bought and paid for by big companies like Monsanto, or General Mills to name a few of the many. Your environmental organizations, your health organizations, such as the EPA and FDA are bought out too. Pretty much anything the US government does, or really most governments as a whole do, you can bet some rich donor or rich company had a hand in making it happen. So yes I think rich donors from the US not only drive Israeli politics, but rich donors drive most politics around the world.
There are only 4 million people in the United States who consider themselves Jewish. That figure represents less than two percent of the American population. Yet somehow, Israel is a huge sticking point in foreign policy with regards to the Middle East. So, it stands to reason there are other factors at work in U.S. policy towards Israel. In addition to monitoring oil supplies, supporting Israel may indeed come from wealthy donors such as Sheldon Adelson and Steven Spielberg.
There are many wealthy Jews in the United States who yield great political and financial influence in both the U.S. and in Israel. With the U.S. as Israel's premier ally in the world, it makes sense that the most influential people in America can have a significant impact on the policies of Israel.
No, I don't believe wealthy donors from the United States drive Israeli politics. From the time that the US gave the Jewish people the land of Israel, they have been close allies, and in fact much of the time it seems that Israel actually drives American politics. Some say this is due to the fact that Israel have important top-secret intelligence and so we act as their lap dog, often supporting their decisions when they bring attacks against Iran.
The long standing belief that American wealth influence the politics of a separate nation, Israel, is borderline insane. There may be an indirection correlation, because some wealthy individuals might have private interests. However, to say that we control their political system is a stretch. Wealthy people can influence any political system at any time they want.