Of course, Uncle Sam can't get involved because the Israelis actually support Assad
Really? I'm not even sure without checking that they have managed to establish diplomatic relations between the 2 countries.
If memory serves, the Israelis launched their strike against the nascent Syrian nuclear capability in about 2008ish and before that, in the Lebanon - Israeli war, Syria threatened to get involved in support of Hezbollah. Plus, Syria is probably Iran's only realy ally in the region, so all in all, hardly a recipe for a beautiful friendship.
You might find that Israel would be prepared to accept a small number of genuine refugees in a controlled manner - far better that than struggling to cope with an influx of all sorts across the borders. But I hardly think that managing a situation equates to supporting them.