The senate must approve any appointment to the Supreme Court. Without their consent, the apointee would not become a member.
The constitution requires that supreme court justices be approved after the president nominates them by "advice and consent". Therefore, the congress can deny the candidate put forth by the president.
Congress has the ability to overrule the President's veto power with a 2/3 majority vote. Furthermore, Congress has the power to impeach the President, and must confirm the President's choices (i.e. appointment of the Supreme Court, etc.). Congress checks the Supreme Court in a few ways as well. First of all, it has to confirm the President's appointments of Supreme Court judges. It also has the power, once again, of impeachment, and has the ability to amend the Constitution.
Checks and balances is the system that allows each branch of government to limit the powers of the other branches. The Executive Branch (the president) can veto a law passed by the Congress and the Congress can veto the law too with a vote of 2/3 of both houses. The Supreme Court can check on Congress by declaring a law is unconstitutional. The power is balanced by the fact that the justices of the Supreme Court are appointed by the Executive branch. The appointments have to be approved by the Congress.
veto
One major check Congress has over the judicial branch is its power to confirm or reject judicial appointments made by the President, including Supreme Court justices. Additionally, Congress can pass legislation that can alter the jurisdiction of federal courts or modify the structure of the judicial system. Furthermore, Congress holds the authority to impeach and remove federal judges, including Supreme Court justices, for misconduct. These powers enable Congress to exert significant influence over the judiciary.
The U.S. Supreme Court has the power to declare an act of Congress unconstitutional.
The supreme court can make sure the president doesn't abuse his power by deeming laws bills passed by the president unconstitutional.
Congress can check the power of the Supreme Court by introducing amendments to the Constitution.
The president has the ability to check the power of the bureaucracy. He does this by vetoing bills that have made it through congress if he disagrees with them. This keeps congress from passing laws unchecked.
The Supreme Court can check the power of Congress by ruling legislation passed by Congress is unconstitutional. The Supreme Court can do this when they a presented with an opportunity to hear a case which disputes a law. The supreme court's decision is final because it is the highest court in America.
Congress can check the executive branch in a number of ways. It can override a presidential veto with a 2/3 majority. It also reviews (and subsequently confirms or denies) presidential appointments (e.g. to the Supreme Court). It also controls the national budget, and - perhaps most importantly - it has the power of impeachment, through which it can remove the President from office.
can propose laws to congress, can veto laws passed by congress, can call special sessions on congress, can make appointments to federal posts, negotiates foreign treaties.