The Executive Branch

Since it is the Supreme Court that decides what is constitutional and what is not, the decisions of the Supreme Court cannot be unconstitutional, however, it is always possible for the Supreme Court to make new decisions which reverse older decisions. So in theory, if the Supreme Court does something wrong, they will be reversed by a later sitting of the same court (but with new judges).

The guiding force in the US for US Supreme Court decisions is the US Constitution. The Supreme Court is one of the three major parts of the Federal government. Through the Congress, the Executive branch and the Court, a balance of power was created.

It doesn't. The president or congress could ignore them to their hearts content, and the court would have no way to stop them.

Congress can attempt to rewrite the law so that it conforms with the Supreme Court's interpretation of the Constitution; or, they can abandon an ill-conceived law; or, they can attempt to call a Constitutional Convention or work with the states to amend the Constitution (the least likely and most time-consuming solution). Congress cannot nullify the Supreme Court decision, however.

In most cases, they either rewrite or abandon the legislation. Congress also sometimes ignores Supreme Court decisions, although they are not supposed to.