Pod Save America had an interesting take on why Kavanaugh is important.
It's not that there aren't other qualified candidates. But despite everything, the core political base the republicans are depending on are still very much behind him. Something like 80% of republicans with the "Trump Supporters" number being even higher.
Combine that with the fact that republicans have had so few wins, a loss here would be devastating for the midterms. A lot of reluctant trump supporters are willing to hold their nose if they get long term wins out of it like a hard right supreme court nominee. A lot of congress critters have bet everything on the Trump bandwagon. If they can't all work together to make Trump look like he's making progress, winning some key battles, some republicans are going to start wondering why they're holding their nose over all these other issues. Would mean bad things in 2020, something like another Tea Party internal revolution for the party in the middle of a term where they're likely to be at very low popularity and can't afford infighting and incumbent primary challenges.
Basically, they're feeling backed into a corner. Or more aptly, have painted themselves into a corner.
Now my take on that is that I feel like that's stretching things a bit as far as how much you can predict the mindset of politicians, and possibly giving them too much credit. But it's a very possible explanation.