Perhaps, after the sinking of the USS Liberty, the US Congress rethinks its support for Israel. (Perhaps it might even retaliate with a different President, though LBJ wouldn't have done so- and Goldwater may not have...)
Alternatively, if the USSR had continued and increased its support of Israel, the US may have been forced to supply the Arab nations, and later, even intervene against Israel.
Finally, if Israel had not adopted a Swiss-style military system, it might be more likely to suffer military defeats, due to its sparse population.