By "gut" do you mean rounding up 60 votes, or pressing the nuke button with 50 votes (I assume Pence can vote to break a tie here, but I am not sure on something that pertains solely to the internal Senate rules)?
The nuclear option. When combined with Democrats, there are technically enough votes in the GOP Senate caucus in regards to upholding traditions like this, but this is a situation where it pits Senate tradition vs the ideological direction of the Supreme Court, which conservatives have been using to achieve their goals for years now. I'm not convinced that they will choose tradition over the USSC.
That being said, personally I wish Schumer would try and squeeze some circuit court picks Mitch blockaded under Obama out of Trump in return for no opposition to his SCOTUS pick. That seems like a wiser choice given the issue of the filibuster, but I guess politically it might not fly well with the base, which expects something that Democrats likely can't deliver.
I've noticed a deafening silence where there used to be con-servative incessant whining and moaning about "legislating from the bench".