Technically, they don't need 60. The cloture rule is what necessitates a 3/5ths supermajority to pass bills, but the cloture rule is not itself a law and so Senators can just... change it with a simple-majority vote. This has already happened twice in the recent past: once in 2013 when the Democrat-led Senate voted to eliminate the cloture rule when nominating federal circuit judges and once more in 2017 when the Ruplican-led Senate voted to eliminate the cloture rule when nominating supreme court justices.
FWIW: Senators tend to really hate doing this. They call it the "nuclear option" because they normally like to get a 2/3rds supermajority agreement before changing any standing Senate rules -- not to mention that the cloture rule itself is often treated as a total third-rail even among the other important Senate procedures. Combining the nuclear option and killing cloture is a massive political powderkeg waiting to explode... but maybe it should?