Yes, President Obama Can Still Nominate a Supreme Court Justice. (Nation, 2/14/2016)
The Constitution does not say that presidents may nominate justices. It says they shall do so.
The Constitution does not say that presidents are limited in this duty by the timing when a vacancy occurs. There is no footnote that says presidents shall only perform their duties in their first terms. Nor is there a footnote that says members of the Senate shall only provide appropriate advice and consent when a president is in his or her first term. And there is certainly no language that suggests that a president’s nominee to the Court must parallel the ideology of the justice he or she would replace.