There are plenty of examples of presidents who supported/signed legislation thinking that the legislation was both constitutional and otherwise good policy.
There are plenty of examples of presidents who opposed/vetoed legislation, thinking that the legislation was both unconstitutional and otherwise bad policy. Andrew Jackson's veto of the Second National Bank is an example of this: he said in his veto message that he believed it was unconstitutional, but he also opposed it on policy grounds.
Both of the above scenarios involve presidents whose policy views lined up with their purported constitutional views. No conflict presented itself.
But here's a challenge for bloggers and commenters everywhere: give an example of a president who opposed/vetoed legislation on the ground that he believed it to be unconstitutional, even though he otherwise supported it on policy grounds? Here the president's view of the proper meaning of the Constitution would be opposed to his view of good policy. To put it in less abstract terms: it would be as if Andrew Jackson had loved the idea of a Second National Bank, but nevertheless vetoed it because he thought it was unconstitutional.
I guess it counts if you can find examples of presidents who supported a policy but opposed specific legislation implementing it on the ground that they believed the Supreme Court would find it unconstitutional, and thus wanted the legislation redrafted to satisfy the Court. But a cleaner example would be one where a president supported a policy but — independent of his view of what the Court might think — believed the legislation implementing it would be unconstitutional.
NOTE: I'm not looking for arguments about whether the president would/could/should do this, and I'm not looking for larger theoretical arguments about the executive role in constitutional interpretation. I'm looking for specific, concrete historical examples that can be supported in the public record.
Are there any such examples?
UPDATE: Thanks to readers for a number of interesting possibilities. Most seem confined to the Nineteenth Century. The one clear Twentieth Century example, President Wilson, is a case where the basis for the president's constitutional objection is the preservation of the executive's own removal power. The disjunction between executive policy preferences and executive constitutional interpretation seems to be very rare.