Думаю, что здесь можно так перевести:

Выдвигая кандидатуру Хейгела на должность следующего министра обороны, Обама сделал шаг навстречу своим политическим оппонентам.

См. значение фразы "reaching across the aisle':
Reaching “across the aisle” is a phrase much bandied about, especially in American politics. The aisle in this case represents the ideological divide between politicians of different parties, especially those who serve in state legislatures or in the federal Senate or House. **When a politician reaches across the aisle, he or she is making compromises with those of the opposing party **in order to write legislation, or cooperate on passing legislation.
http://www.wisegeek.com/what-does-across-the-aisle-mean.htm