A method the Senate has for limiting the power of the Presidency, or preventing the Supreme Court from becoming an extension of the executive branch is not giving two-thirds consent of the Senate.
The Constitutional basis for this is in Article II, Section 2 "...provided two thirds of the Senators present concur; and he shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the Supreme Court..."
