An intuitionist conception of justice is, one might say, but half a conception.

A political conception just applies to the basic structure of a society, its institutions, constitutional essentials, matters of basic justice and property, and so on.

Religious faith is an important aspect of American culture and a fact of American political life.

A comprehensive doctrine, either religious or secular, aspires to cover all of life. I mean, if it's a religious doctrine, it talks about our relation to God and the universe; it has an ordering of all the virtues, not only political virtues but moral virtues as well, including the virtues of private life, and the rest. Now we may feel philosophically that it doesn't really cover everything, but it aims to cover everything, and a secular doctrine does also.

An intuitionist conception of justice is, one might say, but half a conception.

Ideally a just constitution would be a just procedure arranged to insure a just outcome.

Different political views, even if they're all liberal, in the sense of supporting liberal constitutional democracy, undoubtedly have some notion of the common good in the form of the means provided to assure that people can make use of their liberties, and the like.