And more broadly still, if Congress passes a law that violates the Constitution, but the SCOTUS says it doesn't, then pursuant to his OATH, the President is still free to reject the law as unConstitutional. Prove to me that he has a "duty" to violate his oath. I doubt you can.
Well, let's see what it is exactly that we're deal with.
The oath:
"I do solemnly swear (or affirm) that I will
faithfully execute the Office of President of the United States, and will to the best of my Ability,
preserve, protect and defend the Constitution of the United States."
Now what does the Constitution demand of the President? Among other things, (art. 2 sec 3)
"he shall take Care that the Laws be faithfully executed."
It is the Constitutional duty of the POTUS to execute the law.
So, let us imagine a situation in which our theoretical conflict arises.
To begin with, the President certainly vetoed the bill he so disagreed with. He would have no other reasonable first course of action. For the conflict to remain relevant, we must assume that Congress then overrided the veto.
Now the President is in a bit of a quandry, since a Congress united enough on an issue to override a veto (which requires a super-super-majority of
2/3rds of the whole Congress) has the political strength to tear out the President's political nuts over the issue. It would be one thing if the President could be sure the Court would agree with him, since he could then either stall until the law was struck down, or begin implementing it until a case came up for the Court to strike it down, but let's suppose, for the sake of keeping things interesting, that the President is reasonably sure (and he probably could be, in the time it took to get the veto overrid) that the Court would find the law properly constitutional.
In this case, the poor President faces a paradox: insofar as he is required to execute his office, he
must implement the law, but insofar as he required to preserve the constitution, he
must not implement the law.
At this point, I think the only fully conscionable decision he could make would be to remove himself from the situation. And this would happen if he failed to uphold the law anyway, since such a united Congress, with no judicial roadblocks, would certainly remove him for it in due time.
(more realistically, he would probably implement it so half-heartedly that it would barely have an effect, but even then he would be setting up himself, or his party's chosen predecessor, for a crushing defeat at the polls, because I don't think Congress could be so united unless there was similarly massive unity on the issue on the part of the voters)