I’m not sure about needing 3/5 to reject, but I do think that there should be a way for the minority party to call for a vote (If the last few years have shown us anything, it’s probably that the senate majority leader, and likely the speaker of the house as well, have too much influence). I’d rather see a rule that if an issue (whether nomination, law passed by the other house, or proposed legislation) isn’t voted on in a certain number of days (say 30, or even 60 to give committees time) then if enough members (again arbitrary, something like 30 or 40%) formally request a vote it has to be voted on within a week. It could work for nominations, or even for something like the COVID relief acts that have been separately passed. If the two houses of Congress can’t come up with a compromise, make them vote and then have to defend/justify that vote to the electorate. The majority party still has the majority, so they can still vote down anything they don’t approve of, it just gives the minority the ability to call for a vote.

I don’t think it will ever happen, because it would mean politicians actually have to do their job and can’t just point their fingers at everyone else all the time, but I can dream.