The first thing they are worried about is that the Hagel appointment signals an intent to start to slowly roll back American military spending. An American war against most of the rest of the world is no longer supportable under current economic realities. A reduction in American ultra-militarism is not 'good for the Jews', which is to say, not good for continued American support for the building of the Zionist Empire across the Middle East.. Irving Kristol (1984) is remarkably forthright (my emphasis in red):
"Isolationism has a strong traditional appeal to the American people and one can understand why it should reemerge today, or why the prospect of fighting “dirty little wars” in remote places should be so repugnant. What is difficult to understand is why American Jews seem to be among those who are not shocked and appalled by this new trend. Can anyone believe that an American government which, in righteous moralistic hauteur, refuses to intervene to prevent a Communist takeover of Central America, will intervene to counterbalance Soviet participation in an assault on Israel? Can anyone believe that the American people could make sense of such contradictory behavior? Yet a large number of American Jews, perhaps even a majority, appear to believe it.
Have these Jews taken leave of their reason? Of course not. It is simply that their thinking is beclouded by anachronistic presuppositions about the kind of world we live in and about the appropriate responses by the United States to the kind of world we live in. This real world is rife with conflict and savagery. It is a world in which liberalism is very much on the defensive, in which public opinion runs in the grooves established by power, in which people back winners not losers, and in which winners not losers provide the models of the future. In such a world, we are constrained to take our allies where and how we find them—even if they are authoritarian (e.g., Turkey), even if they are totalitarian (e.g., China).
If American Jews truly wish to be noninterventionist, they have to cease being so concerned with Israel, with Jews in the Soviet Union, or indeed with Jews anywhere else. To demand that an American government be interventionist exclusively on behalf of Jewish interests and none other—well, to state that demand is to reveal its absurdity. Yet most of our major Jewish organizations have ended up maneuvering themselves into exactly this position. They cannot even bring themselves openly to support the indispensable precondition for the exercise of American influence on behalf of Jewish interests in the world: a large and powerful military establishment that can, if necessary, fight and win dirty, little (or not so little) wars in faraway places. It is the winning or losing of such wars that will determine the kind of world our children inherit—not striking pious postures or exuding moralistic rhetoric."
The second problem caused by a successful Hagel nomination is perhaps even more profound. For decades now, it has been political suicide to speak the truth about anything. Even once. It is understood that even a sideways reference to the truth, something that might slightly hint at the truth, is the permanent end to your political career. Hagel has on occasion spoken the truth about Israel, Jewish influence on American politics, and crazed American ultra-militarism. If his political career isn't finished, and in fact if the occasional truth actually helps his successful nomination, it will send a signal to the rest of Washington that the truth is no longer completely forbidden. This would not be 'good for the Jews'.