Which Branch is the Authoritative Interpreter of the Constitution?

The Court has just decided Plessy v. Ferguson, which held that racially segregated public facilities were constitutional so long as the separate facilities were equal (e.g. the seats at the back of the bus are the same quality as those at the front of the bus).

Congress then passes a law that requires racial segregation in, say, public transportation. The President vetoes the law and, in his veto message, he says he did so because he believes that Plessy is wrong and, that no matter what the Court says, the Equal Protection Clause forbids racial segregation in public facilities. May the Court rescind the President's veto, because it was based on an erroneous interpretation of the Constitution? Or, at the very least, is the President guilty of irresponsible behavior for refusing to follow the Court's "authoritative" interpretation of the Constitution?

Now suppose Congress passes the law over the President's veto and the President announces that he will not enforce the law because he believes to do so would violate the rights of persons, like Rosa Parks, who choose to violate the law by sitting in "whites only" seats. Is the President's action unlawful or at least irresponsible? How would you advise the President?

Notice that the primary responsibility of the President is to "take Care that the Laws be faithfully executed."  Art. II, section 3 (the "Take Care" Clause).

Consider Prof. Van Alstyne's comments on this issue:

Marbury does not mean, for example, that either Congress or the President need defer to Supreme Court interpretations of the Constitution so far as their own deliberations are concerned and so far as the efficacy of their power does not depend upon judicial co-operation.  When a bill is under consideration, for example, Congress might conscientiously reject the bill believing the bill to be unconstitutional even assuming that the Court has provided no precedent for that belief and even assuming that the Court has upheld similar legislation adopted by an earlier Congress.  Similarly, the President may veto the bill on the grounds of his own interpretation of the Constitution – whether or not it is the same as the Court’s.”