According to the New York Times:

Mr. Obama answered a question about “dealing with the hawks in the current Israeli government,” by suggesting that Israel’s new, conservative prime minister, Benjamin Netanyahu, might have an opportunity to play a more constructive role than a more liberal leader:

I believe that Prime Minister Netanyahu will recognize the strategic need to deal with this issue. And that in some ways he may have an opportunity that a labor or more left leader might not have. There’s the famous example of Richard Nixon going to China. A Democrat couldn’t have gone to China. A liberal couldn’t have gone to China. But a big, anti-communist like Richard Nixon could open that door. Now, it’s conceivable that Prime Minister Netanyahu can play that same role.

This is the essence of  Cukierman and Tomassi’s “Why does it take a Nixon to go to China?” American Economic Review, Mar. 1998, pp. 180-197.  Suppose a political knows the “state of the world” and the policy that most voters would support.  But voters do not have this information.  They cannot tell whether a policy is suggested by a politician because it is the ideal policy for the state of the world or because he has a bias for it.  Then, a right-wing politician is more likely to implement a extreme left-wing policy. Voters are likely to believe it is the “right” policy as he is voting against his natural bias.  He is then rewarded by being re-elected.  Hopefully, there is no Watergate on the horizon for Netanyahu.