Perhaps Cruz is only being Machiavellian. If becoming President of the United States means I have to accept the (artificial) support of the RINO-Whigs, so be it. If elected, he can always write much of his own script anyway.
He will never get my vote at this point.
I also do not believe it to be possible for him to take office even if he won an election.
With the loss of Scalia, the Democrats will challenge his eligibility, it will go to the courts, and there would be zero paths to get a Ted Cruz inauguration through the at best deadlocked supreme Court.
Obama would remain in office for the interim.