My expectation is that this will motivate them to pull another Ross Perot. They will spend all of their time working with Republicans between this election and the next dreaming up institutional hurdles to a socialist making headway in a political campaign, just like they made it institutionally impossible for third parties to sniff a presidency.
If Mamdani actually does try to do the things he says he will (which I doubt) those efforts to institutionally hamper non-conservative candidacies will be doubled.