Bryan offers the most extensive version of his view I've seen him blog. On overall method and meta-ethics, I'm not so far from Bryan (and someday he will get a post in praise of him). But I usually disagree with his applications of the method. For instance he seems to argue that because employees are allowed to discriminate against employers, we should allow for a reciprocal right of employer discrimination.
My first objection is that we cannot judge an argument like this outside of a particular historical context. In some cases employer discrimination rights may be fine, in others not. I don't think ethical intuitionism, as could be represented by abstract reasoning from analogy. can do the hard work here. Rather we must look to the history to understand the meaning and long-term effects of the discriminatory act under question. In some cases the discrimination is effectively perpetuating a regime of evil and thus it is morally wrong.
Here is another part of Bryan's argument:
Suppose A and B be are dating. A has an equally good outside option.
B can't bear to live without A. A therefore has some bargaining power
– vastly more than most employers, in fact. Yet almost everyone thinks
it would be wrong to force A to stay with B.
If there is one intuition that many reasonable people have, it is that family and personal relationships are not, in moral terms, exactly like commercial or work place relationships. I get nervous when I see ethical intuitionists serve up simple analogies across these various realms. (In general I think Bryan creates too much license for analogical reasoning of this kind.) This is also why I am not convinced by all of the arguments in Steve Landsburg's Fair Play.
My overall view is that ethical intuitionism settles many fewer issues than most of its proponents like to think. That said, there is often nowhere else to go. We somehow need to come to terms with two propositions at the same time:
1. We need to think more rather than less ethically.
2. The content of ethical philosophy tells us less, in reliable terms, than most people would like to believe.