Obama administration officials have been on the telephone almost daily with their Israeli counterparts urging them to “please chill out,” in the words of one senior administration official, as President Obama has raced to respond to the rapidly unfolding events.

But the crisis raises many questions about how the United States will navigate its relationship with Israel — in particular the balance between encouraging the development of a democratic government in Egypt and the desire in Washington not to risk a new government’s abandoning Mr. Mubarak’s benign posture toward Israel…

“The Israelis are saying, après Mubarak, le deluge,” said Daniel Levy, a former Israeli peace negotiator. And that, in turn, Mr. Levy said, “gets to the core of what is the American interest in this. It’s Israel. It’s not worry about whether the Egyptians are going to close down the Suez Canal, or even the narrower terror issue. It really can be distilled down to one thing, and that’s Israel.”