American exceptionalism does not allow for America to be ruled by any "global governance".

The ideas do conflict, but there is nothing logically exclusive about American exceptionalism and global governance. For instance you can believe that America is the last, best hope of earth, or "the indispensible nation", or history's shining moral beacon, and still think it is worthwhile to sign and abide by treaties and support the UN. Much of international law has been shaped by the US. By and large, outright opposition to global governance has come from the post-1994 Republicans.

Signing up to the Kyoto successor treaty and the International Criminal Court are critical tests for the next US President.