Well they don't literally control the votes, but folks by and large vote for who the party supports. The scenario is closer to something like you ran for office with the party's support and got elected. Then it's election time and now the party goes and gives money to someone else, helps them fundraise, gets them in touch with your previous donors (now no longer your donors), and now your election went from a pretty easy shoe-in to an all-out fight for you to secure your job against the entire party apparatus. Whereas if you toe the line, none of that has to happen.
So in short, yes the parties can and do find various ways to discipline those who don't fall in line. This is something that is obviously* true.
> Party funds are often less significant than both candidate raised and outside funding, so while that's true, its not a particularly strong sanction.
* Here it is important to understand where campaign funds come from. It's not about the money coming from party funds, it's the connections the party has to help you the candidate acquire additional funds from donors and donor organizations, introductions, etc.
Nor do they control whether someone does or does not file for election as a primary candidate against you, nor do they control whether a primary challenger is able to mobilize the parties usual voters.
> but folks by and large vote for who the party supports.
If by "who the party supports" you mean "either the incumbent, if there is one, in the primary or whoever wins the primary in the general", you are correct, but that...doesn't address the issue.
If you mean, "who the party leadership supports, irrespective of incumbency and other factors, in the primary", that's not really strongly the case in normal party primaries. (It's kind of true in Republican primaries in the era of Trump, but that's a result of a powerful outside-of-leadership activist movement taking over the party leadership that was strong enough to defeat the leadership's candidates in primaries taking over the party leadership, but that's...not an easily replicable condition, and the only reason it could happen is because party leadership doesn't control who gets primaried, at all or who successfully.)
Trump is an unusual factor, he's able to kick a lot of people's asses who other people couldn't kick. The same people who got attacked on Jan 6 couldn't discipline him for that.
My understanding is that since the Tea Party, Republican house members haven't lasted as long as house members usually have because they either decide the juice isn't worth the squeeze or get primary challengers.
Bigger picture, Tillis resigning is bad news for the Republicans in the sense that, in the current climate, he's likely to be replaced by an extremist just when people are going to be sick and tired of the consequences of Republican rule (e.g. just as people were sick and tired of Democratic rule not long ago.) No party has the Democrat's ability to pull defeat from the jaws of victory but if they can put up somebody who doesn't use words like misogynoir and latinx against somebody far to the right of Tillis the outcome will be predictable.
One form of "party discipline" I noticed in 2016 was that primary candidates from the presidency made the tour of right-wing donor organizations that would make them kiss the ring and run the gauntlet, testifying that they pass a long list of "litmus tests" that I think weren't all that popular with voters, even conservative voters. Trump stood out because he was the exception, and in particularly he brought up the immigration issue which was otherwise suppressed by the system. My interpretation though was that the Republican Right was funding a large number of "no hope" candidates and there was some combination of "these organizations win by getting a lot of coverage for conservative ideas in the media" and "these candidates get a lot of money they can spend to hire their friends to work on their campaigns"
Well they don't literally control the votes, but folks by and large vote for who the party supports. The scenario is closer to something like you ran for office with the party's support and got elected. Then it's election time and now the party goes and gives money to someone else, helps them fundraise, gets them in touch with your previous donors (now no longer your donors), and now your election went from a pretty easy shoe-in to an all-out fight for you to secure your job against the entire party apparatus. Whereas if you toe the line, none of that has to happen.
So in short, yes the parties can and do find various ways to discipline those who don't fall in line. This is something that is obviously* true.
> Party funds are often less significant than both candidate raised and outside funding, so while that's true, its not a particularly strong sanction.
* Here it is important to understand where campaign funds come from. It's not about the money coming from party funds, it's the connections the party has to help you the candidate acquire additional funds from donors and donor organizations, introductions, etc.