Mr. Netanyahu, his close associates say, desperately wants Mr. Obama to use the diplomatic muscle of the United States to protect Israel from the vote, not only by vetoing it in the Security Council, but also by leaning hard on America’s European allies to get them to reject it as well.

Mr. Obama has indicated that he will certainly do the first. But it remains unclear how far Mr. Obama can go to persuade Britain, France and other American allies to join the United States in rejecting the move, particularly as long as Mr. Netanyahu continues to resist endorsing the pre-1967 lines.