Article II, Section 2 is clear enough:
[The President] shall have Power…, by and with the Advice and Consent of the Senate, shall appoint… Judges of the supreme Court….
Simple. The question is, will he take the advise of the Senate before he nominates someone.
According to David Savage, Supreme Court correspondent with the Los Angeles Times and Chicago Tribute, Reagan presented a dozen candidates to the Senate Judiciary Committee. One of those candidates was Robert Bork. Sen. Biden, then the Chairman of that committee, told Reagan that Bork was not acceptable. Reagan nominated him anyway, and his nomination was rejected. Reagan then nominated Kennedy, whom Biden said was acceptable, and he was approved 97-0.
The role of the Senate is also clear. There is no requirement for the Senate to confirm an objectionable nominee.
So, 0bama has to make a choice. He can nominate a left-wing lunatic with no respect for the Constitution whatsoever (yes, I’m being redundant), and try to brow-beat enough RINO’s into confirming him/her. If he fails, the next president will choose the next member of the Supremes. Or, he can nominate someone who is not a left-wing lunatic and who does respect the Constitution, embarrass any Republicans who refuse to give him a vote, and possibly get to appoint the next Associate Justice.