it's really just a matter of whether the president is willing to do his job. the president's main role under the constitution is as the executive. and that means that it's his job to enforce (i.e. to execute) the laws of the united states.
which is why a president who signs a law but attaches a statement saying that he won't enforce the parts he doesn't like is essentially admitting that he is not willing to perform all his job duties.
if he doesn't want to do all the things a president is supposed to do, he can always resign.
