I realize there's no shortage of hypocrisy among politicians (and in my view particularly among the social conservatives), but I'd really like to hear how the supposed "strict Constitutionalists" a-la Ted Cruz defend the view that the Senate should refuse to even vote on any nomination until the current President is out of office. And that "the American people" should decide (via the next election) who gets nominated [to replace Scalia]. Can they please point out the part in the Constitution where it says that? Or where the people didn't already decide to elect Obama, twice? For God's sake, Scalia himself was a strict interpreter of the Constitution, yet they advocate going completely outside its confines to replace him?
First off, a disclaimer that I am one who thinks the nomination/confirmation process should move forward as usual. I do not agree with Cruz's position.
Second, though, to answer your question, there is nothing in the Constitution that prohibits this from happening -- meaning the Senate is not required by the Constitution to actually vote on the President's nomination, and the Senate can prevent the confirmation process from proceeding to the final vote.
(A) The confirmation process itself is not explicitly addressed by the Constitution beyond what is specified in Article II, Section 2, Clause 2, providing:
[The President] shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, 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, and all other Officers of the United States, whose Appointments are not herein otherwise provided for, and which shall be established by Law: but the Congress may by Law vest the Appointment of such inferior Officers, as they think proper, in the President alone, in the Courts of Law, or in the Heads of Departments.
(B) The Constitution also grants the Senate various powers for conducting its business, including, under Article I, Section 5, Clause 2, that "Each House may determine the Rules of its Proceedings." Under the Rules of the Senate, the President's nomination of any federal judicial appointee would go through the Senate's Judiciary Committee. Specifically, Rule XXV.1(l).10 provides:
1. The following standing committees shall be appointed at the commencement of each Congress, and shall continue and have the power to act until their successors are appointed, with leave to report by bill or otherwise on matters within their respective jurisdictions: . . .
(l) Committee on the Judiciary, to which committee shall be referred all proposed legislation, messages, petitions, memorials, and other matters relating to the following subjects: . . .
5. Federal courts and judges.
(C) The Rules of the Judiciary Committee are published here:
http://www.judiciary.senate.gov/about/rules They include items such as:
At the request of any member, or by action of the Chairman, a bill, matter, or nomination on the agenda of the Committee may be held over until the next meeting of the Committee or for one week, whichever occurs later.
(I.3.)
The Chairman shall entertain a non-debatable motion to bring a matter before the Committee to a vote. If there is objection to bring the matter to a vote without further debate, a roll call vote of the Committee shall be taken, and debate shall be terminated if the motion to bring the matter to a vote without further debate passes with eleven votes in the affirmative, one of which must be cast by the minority.
(IV.)
Thus, the Senate also has the constitutional power to put the nomination through the Committee, which also has the constitutional power to delay voting on the nomination indefinitely so long as they have sufficient number of members who want further debate.