Gen. Martin E. Dempsey, the chairman of the Joint Chiefs of Staff, is in Israel and via FP's Situation Report refers to the NYT article, his own words:
an outreach to other partners who may not have been willing to be partners in the past..What I mean is the Gulf states in particular, who heretofore may not have been as open-minded to the potential for cooperation with Israel, in any way.
Then others said, with my emphasis:
While General Dempsey did not go into specifics, other American military officials said that possibilities include intelligence-sharing, joint counterterrorism exercises and perhaps looking for how Israeli and Saudi troops could jointly work on the training of Syrian opposition fighters
Link:http://www.nytimes.com/2014/04/01/wo...01%202014&_r=0

Clearly someone has not thought this idea through, particularly how our shared enemies would respond. Let alone IMHO the reaction within both countries.