I think poster is referring to the fact that the U.S. gives Israel almost 4 billion dollars in aid a year.
It's not that Israel has infiltrated America but instead the fact that American politician do not expect to be electable unless they behave as a "friend to Israel" given certain jewish and christian communities are willing to campaign against politicians on this issue.
This means the Israeli representatives can even come to the U.S. and act like belligerent a-holes and the politicians have to put up with it to win elections.
If the poster was really suggesting infiltration rather than being sarcastic I would assume they are perhaps trading in antisemitic conspiracy theories.
I wouldn't think it's that one. They definitely have huge influence, but the country that I think of as having actually infiltrated the US government is a different one in that part of the world.