On NPR yesterday I heard him say more or less what is reported here, that according to the Constitution the Senate "is to consider that nomination and either they disapprove of that nominee or that nominee is elevated to the Supreme Court" [my emphasis].
Not true at all. There's no such duty, constitutional or otherwise. There's no mention at all in Article II. Section 2 that the Senate is to do this, so the President is wrong on a second count in his "amusement" of strict constructionists:
"I'm amused when I hear people who claim to be strict interpreters of the Constitution suddenly reading into it a whole series of provisions that are not there," Obama said.
"The Constitution is pretty clear about what is supposed to happen now," Obama, a former constitutional law professor, told a news conference at the close of a two-day meeting with leaders from Southeast Asia.
Implied is that what he is saying is correct even on strict constructionist grounds (rather than on "living breathing" grounds where whatever a living Democrat says that it says or means is true). Article II. Section 2 is vague other than to say "by and with advice and consent" from the Senate. But no rules are laid down for how this should be done--nothing about giving an up or down vote--and each House can determine its own procedural rules. So the President is wrong--probably lying--and the Senate is within its Constitutional right to (e.g.) filibuster.