The constitutional issue at the heart of united states v. nixon is best described as
whether the supreme court could hear the case.
the right of a president to resist impeachment.
the extent to which the separation of powers was allowed.
whether laws had been broken during the watergate incident.

I believe the answer is: whether the Supreme Court could hear the case.

At that time, President Nixon wanted to use his Executive previlege to avoid the supreme court from hearing his case and argued that it's all for the sake of national security. The court ruled against nixon and ordered him to hand over the tape which lead to his impeachment during the watergate scandal.

the  wilmot proviso  was designed to eliminate  slavery  within the  landacquired as a result of the mexican war (1846-48). fearing the addition of a pro-slave territory, pennsylvania congressman david  wilmot proposedhis amendment to the bill.