As others have pointed out, in strict application of recusal rules, there has to be a case first - no case, no question of recusal.
The public will decide if Cruz can be impartial in vetting a nominee, if one should be advanced and be subjected to a committee vote. There is no rule that forces him to recuse, not even if there WAS a case underway that involved him, that was in fact before SCOTUS. He's not the judge. He can pick a judge that he KNOWS will rule in his favor, and it would be up to that judge to recuse him or herself, again, as conscience and care for appearance of impartiality may guide.
The fact is that a US Senator does not have to be, nor is required to by the Constitution, to be ‘impartial’. The requirements for being Senator are finite and written clearly. The responsibility any Senator owes is to the state which he represents and the nation as a whole. Partisanship, preferences, biases or proclivities not reaching the definition of impeachment are at a Senator’s discretion.
In truth, the public won’t decide crap about Cruz’ authority to vet; that is ALREADY given by his being a Senator. It is up to those who want Obama’s choice, likely a very bad one, to get enough Senate votes to overcome dissent.
What the author asserts is bullshit and it is a diversion and attempt at influencing this Senator’s standing in election for higher office as well as intimidate him to change his likely opinions and advice and consent on a duty he is already sworn and authorized to execute. The Constitution says nothing about all these specious suppositions of IFs, CANs or MIGHTs, and it is a waste of time to suffer the machinations of these fools any further than right now.