A reasonable assessment of the founder's intent says you're simply wrong about the Constitution.
The key phrasing in question is...
"[The President] shall have Power, by and with the Advice and Consent of the Senate...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"
First of all its rather clear Obama would be outright failing in his constitutionally required duties if he didn't pick a nominee since the phrasing is "shall nominate" rather than leaving it optional or the like. Especially as the founding father's were clearly thinking of things, the "advice" part requires the Senate to actually consider and debate the specific nominee so the President can at least know the reasonably grounds the Senate happens to object to that specific nominee.
Its also incredibly clear that for instance James Madison was certainly not thinking of a party arbitrarily blocking consideration of any nominee for essentially a year while hoping their candidate wins the Presidency when he was involved with writing the provision that way.
(For a historical early example of a late term Supreme Court appointment, John Marshall was nominated as Chief Justice of the Supreme Court on January 20th of 1800 and confirmed on January 27th, while John Adam's time as President ended on March 4th of 1800. While Thomas Jefferson came in as the opposing party's candidate for President and was not happy with the nomination, he accepted it and certainly never suggested something like the Constitution didn't envision a President nominating and confirming new court vacancies late in their term.)