Steven Lubet is a professor at Northwestern University Pritzker School of Law. His most recent book is " The 'Colored Hero' of Harper's Ferry: John Anthony Copeland and the War against Slavery ." The opinions expressed in this commentary are his.

(CNN) Despite the objections of Senate Majority Leader Mitch McConnell, President Obama has announced his intention to submit a nominee to fill the Supreme Court vacancy created by the death of Justice Antonin Scalia.

And despite Donald Trump's call for "delay, delay, delay," the Senate Judiciary Committee will almost certainly have to hold a hearing on Obama's eventual nominee.

It would be one thing to vote against an individual, or even to stage a filibuster, but quite another to abdicate the Senate's constitutionally required "advice and consent" function by refusing to extend even the minimal courtesy of a committee hearing.

That brings us to Ted Cruz, who happens to be the only remaining Republican presidential candidate with a seat on the Senate Judiciary Committee. Under ordinary circumstances, Cruz would therefore be entitled to question the eventual nominee, and to vote on whether his or her name should be advanced to the Senate floor.

Cruz, however, has an unresolvable conflict of interest in this matter, which should disqualify him from participating directly in the proceedings.

As is well known, Cruz's claim to "natural born" United States citizenship has been questioned (bombastically) by Donald Trump, and (very seriously) by a number of highly respected legal scholars, including Harvard's Lawrence Tribe and the University of Chicago's Eric Posner.

It is far from a given that Cruz is constitutionally qualified to be president, and his status, if nominated, is sure to be challenged in court. (The one case already filed was an easily dismissed nuisance suit, but serious litigation would certainly follow from an actual Cruz nomination.)

Such a case would ultimately reach the U.S. Supreme Court, which gives Cruz a unique stake in filling the current vacancy. If Cruz were to remain an active member of the Judiciary Committee, he would actually have a chance to interrogate -- and to vote upon -- his own potential judge.

Although never known for rhetorical restraint, candidate Cruz would probably refrain from blatantly grilling Obama's nominee on the meaning of the "natural born citizen" clause, but virtually any other question about constitutional interpretation would still have implications for the legitimacy of Cruz's campaign for the presidency.

What does the nominee think about originalism? What sources would he or she consider when interpreting the Constitution? How important is precedent when facing a novel issue? Every question and answer would be read subtextually for its impact on Cruz's citizenship status.

Even something entirely anodyne -- say, reading the bedtime story "Green Eggs and Ham," as Cruz did in an earlier filibuster -- would have to be seen as a strategic attempt to delay or derail a potentially unfavorable decision on his own qualification for office.

If allowed to participate in the committee hearings, Cruz would likely be the first senator in history to question a Supreme Court nominee with his own future so clearly affected by the outcome of the hearing. The circumstances are so unusual, in fact, that they are not even contemplated by the Senate's Conflict of Interest rules.

Senate Rule XXXVII prohibits senators from advancing "the progress or passage of legislation, a principal purpose of which is to further only his pecuniary interest," but it is silent on using committee hearings to gain a potential, and highly personal, advantage in impending litigation.

For better guidance, we might therefore turn to the Code of Conduct for United States Judges , which requires disqualification whenever a judge has an "interest that could be affected substantially by the outcome of the proceeding." Although the Code of Conduct was not written with legislators in mind, it seems particularly apt in this instance, where Cruz would be in the position of virtually passing judgment on his own judge.

While there is no rule or code provision that specifically applies to Cruz's situation -- which, after all, is unprecedented -- the very term "conflict of interest" implies a strong ethical norm of recusal when one's personal interests may be at stake in a governmental proceeding. Moreover, there is no compelling reason for Cruz to participate in the hearing; the committee could function perfectly will with a Republican replacement appointed by Majority Leader McConnell. Any decision at the committee level -- either for or against Cruz's involvement -- would afterward control his participation in the event of a floor vote on the nominee.

JUST WATCHED The fight for Justice Scalia's replacement is on Replay More Videos ... MUST WATCH The fight for Justice Scalia's replacement is on 02:17

The Senate Judiciary Committee is currently chaired by Sen. Charles Grassley of Iowa, who is well regarded on both sides of the aisle. Along with virtually every other Republican, Grassley has called upon the President to refrain from putting a name forward for the SCOTUS seat, stating -- incorrectly, as it happens -- that "it's been standard practice over the last nearly 80 years that Supreme Court nominees are not nominated and confirmed during a presidential election year." In 1988, the Senate confirmed President Reagan's nomination of Justice Anthony Kennedy, who had been nominated the previous year. Although the Senate was then controlled by Democrats, there was no concerted effort to stall the nomination until after the November election.

Grassley has not, however, declared that he will refuse to hold hearings on an Obama nominee, and for good reason. Respect for the Senate's constitutional role, and for the Supreme Court itself, all but requires that a presidential nominee be given a fair hearing even if he or she will ultimately face rejection.

But the emphasis has to be on "fair," which ought to exclude Ted Cruz from participating. I have no firm opinion on whether Ted Cruz is a natural born citizen and thus eligible to be elected president, but I do know that he should not be allowed to select --- or de-select --- his own judge when the decision on his presidential future may well hang in the balance.