Ted Cruz and his allies will say that the loss was the predictable result of failure to nominate a true conservative. Faced with two essentially similar candidates like Donald Trump and Hillary Clinton, conservatives chose to stay home. To win in 2020, they will say, Republicans must abandon moderation and the desire for "deals" and nominate a stalwart, no-compromise conservative like Cruz.
Establishment Republicans will say the problem is that the party let the clowns take over, and must return power to the adults in the room like Jeb Bush and Marco Rubio, instead of toxic candidates like Trump and Cruz. They will not address the problem that orthodox Republican policy prescriptions are unconvincing even to voters in the Republican primary, let alone the general electorate.
Trump and his fans will say that the Republican establishment sabotaged Trump by withholding their support, hoping they could quash his insurgency by manufacturing a wide loss to Hillary Clinton. They will not go away quietly.