I read this somewhere a long time ago about how they do this.
Basically, the Democrats made a big issue of Betsy DeVos because they think it'll make it easier to win future elections.
The Republicans understand what the Dems are doing. They also know they have two votes to allocate to vulnerable members. Just two will get leave to vote against DeVos. Lots of factors determine who. How likely they are to win re-election. How reliable they are. Favors they are owed. Their ability to raise money. Do important lobbyists like them?
Some people think, imho erroneously, that they voted against DeVos out of principle. Maybe they really do believe she'd be a bad Secretary of Education. But first and foremost they are Repubs. Their No vote was not an act of rebellion. It was part of a Repub strategy to remain in control of the Senate.
All the theater the Dems put up over this was also for the purpose of winning future elections.
The takeaway is this. Nothing will change how politics works in the Senate. But we the voters have the ability to move them in different directions based on how they think we'll vote. Also factor in whether they think we will or can vote.
That's the system. Think about manipulating it to get what you want. And for that you have to team up with lots of other voters, because that's what counts, massive numbers of votes, in the right places. That will change the calculations of the parties in Congress.