Nikki Haley would be the presumptive frontrunner for the 2020 GOP nomination and it would be increasingly clear she'd win. The GOP would be on the verge of winning control of enough state legislatures to call and control a constitutional convention, and there would be a serious movement afoot to do so. The GOP would have a veto on any and all legislation and the grassroots GOP would heavily pressure party members not to pass anything support by Clinton. The GOP would be in an even better position for the Senate than they are now.
PRetty much this, but I fear that it would be someone more extreme like Tom Cotton or Ted Cruz instead of Nikki HAley.
Regardless we would be effectively a one-party state due to the impotence of the Democrats in this scenario.