I would argue that the Senate has an affirmative duty to accept or reject candidates put before it. If the Senate were to pass a rule at the start of its term mandating that all candidates would be rejected if they did not receive unanimous consent, I would argue that would be constitutional, but the purpose of a filibuster is not to accept or reject candidates, but rather to keep them from being acted upon one way or the other. And that, IMHO, constitutes deriliction of duty.
Filibustering of legislation generally does not pose the same problem, btw, because with very few exceptions there's no constitutional imperative to pass or even consider legislation. To be sure, I don't think congresscritters would have much fun if they never considered any legislation beyond what was Constitutionally required, but postponing indefinitely the discussions of non-required legislation falls entirely within legislative prerogative.
In reality, the purpose of a filibuster is to reject the candidate. If it drags on too long for the President's tastes, nothing's stopping him from withdrawing the nomination and nominating someone else. Operationally, it's the same as it would be if the Senate's rules mandated rejection if 60 votes weren't attained.
Filibustering of legislation generally does not pose the same problem, btw, because with very few exceptions there's no constitutional imperative to pass or even consider legislation.
If the Senate leadership refused to take up the consideration of a nominee for a position, that would not be unconstitutional. That actually happened during Clinton's presidency, when he tried to nominate William Weld as ambassador to Mexico. Jesse Helms headed the Foreign Relations Committee, and refused to schedule hearings for Weld, who eventually withdrew.
But the bottom line is that if the Constitution can require a simple majority in one case without actually saying so, then it would have to require it in all cases where Congress is given power to act. Otherwise, insisting on a simple majority for confirmations is just a contrivance for preventing delays. In that case, then, what's really being argued is that the delay itself is unconstitutional, which means it would be unconstitutional regardless of what causes it.