The Executive Branch
No, Congress cannot directly overrule decisions made by the Supreme Court. The Supreme Court's decisions are final and cannot be overturned by Congress.
No, Congress cannot override decisions made by the Supreme Court. The Supreme Court is the highest court in the United States and its decisions are final and binding.
The President of the United States, who currently (in 2013) is Barack Obama, has the responsiblity of carrying out the laws enacted by Congress as interpreted by the Supreme Court.
No, a Supreme Court ruling cannot be overturned by Congress. The Supreme Court is the highest court in the United States and its decisions are final and binding. Congress does not have the authority to overturn a Supreme Court ruling.
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).
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.
The decisions of the Supreme Court can be overturned through a few ways, such as passing a constitutional amendment, the Court itself reversing its own decision, or Congress passing a new law that contradicts the Court's ruling.
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.
The Supreme Court
The decisions of the Marshall Court established the Supreme Court as a branch of government equal to Congress and the Presidency.
The US Supreme Court lacks the ability to enforce its own decisions, which is a check on the Judicial Branch of government. The Executive Branch is vested with the authority and obligation to enforce Supreme Court decisions, and the Legislative branch can support a decision by passing laws upholding the Court's finding.
The Legislative (Congress) and possibly Executive branches would benefit if Congress had the power to nullify US Supreme Court decisions, because their power would then be unchecked by the Judicial branch. Such authority would violate separate powers established by the Constitution to ensure no single branch of government becomes too dominant, and would allow Congress to ignore the Bill of Rights and other Amendments, to the detriment of US residents.