I see that the statement by 8 former OLC members on the Georgetown Law Blog makes a similar claim, with respect to the non-enforcement power and the line-item veto, to the one I made below:

We agree wholeheartedly that a President cannot simply choose not to enforce whichever statutes he does not like. A President may not exercise a dispensing power—in effect a type of “line-item-veto”—to ignore statutes that he thinks are unwise, or wrong, or politically inexpedient. ... The President has an obligation under Article II to faithfully execute the laws.

But that "Take Care" obligation includes a responsibility, above all, to faithfully execute the Constitution.Thus, in some limited and relatively rare circumstances, the President might best fulfill his constitutional obligation by refusing to enforce a statutory provision that he considers to be unconstitutional.