I disagree, but save an in depth explanation for later, if at all. I went around with Huck on this last week.
The Rules provision in the Constitution cannot be fairly extended to admit changing the balance of powers between the various branches, which this 60 vote arrangement does. If you devolve to a literal read of the COnstitution, you can assert that the Senate has no obligation to seat any part of the President's cabinet, or a court, or to hold an impeachment trial if articles of impeachment are sent from the House. The language in the Constitution is "shall have the sole power to ..." - not "has a duty to ..." Literally taken, it will destory our system of checks and balances.
They don't. Here's an example from US History when they chose NOT TO ACT AT ALL:
Few Presidents have had a rougher time filling vacancies on the Court than John Tyler. His first maneuver, upon the death of Justice Smith Thompson, was to offer the position on the Court to Martin Van Buren, who was the leading candidate for the Democratic presidential nomination which Tyler hoped to claim for himself. But that crude effort to immobilize a rival was squelched before any nomination was made, and when Tyler named John C. Spencer of New York, the irate Whigs of the Senate rejected him. The President's next move was to offer this position to two Philadelphia lawyers apparently because he was impressed by the arguments they had just made in a case before the Court. When John Sergeant declined on grounds of age and recommended his fellow townsman, Horace Binney (at the same time swearing the President's emissary to secrecy about the prior offer to him) a tender was made to Binney, who declined for the same reason and recommended Sergeant, with a plea that his own declination never be disclosed. Tyler then twice offered the judgeship to Silas Wright, Democratic leader of the Senate, who twice declined. In desperation, Tyler sent the name of Reuben H. Walworth, Chancellor of the State of New York, to the Senate in March, 1844. When a second vacancy on the High Bench occurred, Tyler offered the position to James Buchanan, who declined, and then nominated Edward King of Philadelphia. On the last day of its session the Senate laid both nominations on the table. Trying once more in the last days of his administration, Tyler withdrew the King and Walworth nominations and sent in the names of John Meredith Read of Philadelphia and Samuel Nelson of New York. Nelson was confirmed and served on the bench for twenty-seven years, but the Senate did not act on the Read nomination. Only one of Tyler's ten tries was successful. (See "Robin Hood, the Supreme Court and Congress," in Yearbook 1978.)
At times rejection by inaction has been far more common than rejection by up or down vote. One study of the Senate's exercise of the advice and consent power found that during a twenty year period from 1929-1948, the Senate rejected 15,263 presidential nominations through inaction. In the same period only 84 nominations were rejected by straight up or down votes.13 Such large numbers rejected without a vote are not an aberration. In 1917, roughly 2000 of President Wilson's nominations were blocked through the end of the session due to senatorial unrest over his nomination of his personal physician (Dr. Cary Grayson) to be a Rear Admiral.Rejection by failure to take a final vote has frequently defeated judicial nominations and executive branch nominations. For example, in 1828, the Senate Committee tasked with considering judicial nominations on at least one occasion expressly found that it was within the authority of the Senate to decide that it was “inexpedient to advise and consent to the nomination now” and to therefore take no action, killing the nomination after the Senate adjourned.
Deliberately denying a Supreme Court nominee an up or down vote in the Senate appears to be particularly common. Of 24 nominations to the U.S. Supreme Court whom the Senate did not confirm between 1789 and 2002, 14 (nearly 60%) were defeated through inaction or delay.16 These 14 defeated without an up or down vote represent nearly 10 percent of all the Supreme Court nominations made in our nation’s history.
As one scholar of the Senate wrote in 1938, “The Senate, on its part…has often taken no action upon [a nomination], or, after long delay, has voted to postpone its consideration indefinitely. At least ten nominations to the Supreme Court have been blocked in this way.”
Such was the fate of Andrew Jackson Supreme Court nominee Roger Taney on President Jackson’s first attempt to nominate him. The Senate held up the nomination for six weeks and then voted to indefinitely postpone a final confirmation vote. Reportedly, when President Jackson heard the news, well after midnight, that the Senate had defeated his nominee by inaction he referred to the body as “damned scoundrels.”19 Taney was later renominated and confirmed as Chief Justice.
Other 19th century examples include President John Tyler’s nominations of Judge Edward King and Reuben Walworth to the bench which were blocked in the Senate for over a year until he finally withdrew them. After he submitted two new names for the bench (John Meredith Read and Samuel Nelson), the Senate confirmed Nelson but refused to take final action on Read.
And that's just a sampling.