I believe that Jefferson would state that every generation can define marriage as they wish. In fact, I believe he would go further and state that it is none of our business how people 100 years from now want to define marriage.
Would you give this power to the executive? Would you allow the executive branch to decide if something was constitutional or not?
I would insist that the executive decide whether something is constitutional or not before acting.
How than could you stop illegal searches? All the executive has to do is declare them "not illegal."
I would insist that judges (like all other constitutional actors) consider the constitutionality of what they do before they do it. If a court believes that a prosecutor is attempting to admit into evidence items that were recovered by an unconstitutional search, the court should refuse to allow the prosecutor to do so. The court should not permit its operations to be tainted by unconstitutional conduct. In other words, the court (as a co-equal branch of government) has the inherent power to refuse to participate in unconstitutional activities.
If the Executive is conducting illegal searches and not attempting to use the materials in court, the Congress would retain the power to cut off funding for the activity and/or the courts can award damages to parties who are injured by such illegal conduct. I think if you consider various potential problems, you will find that most government activity will require the tacit support of at least two of the branches to sustain it over a period of time. The key is that every branch has an obligation to consider its constitutional responsibilities.
Would you give this power to congress? They routinely make anti-constitutional laws, and don't ever seem to have the wit to realize that's what they are doing. Either that, or they just don't care.
I would insist that the Congress decide whether something is constitutional or not before acting. The fact that the Congress passes an unconstitutional law does not mean that other branches have to participate in its enforcement. Each branch should be considering the constitutionality of what it is doing.
The founders deliberately insulated the courts from the passions of the people, but I think they did not consider the degree to which this would create these petty tyrannies and partisan results in the courts.
You will look long and hard before you find any provision in the constitution that states that the judiciary has greater power than other branches to interpret the constitution. This why Jefferson regarded Marbury v. Madison as a judicial usurpation.
I believe that Jefferson would state that every generation can define marriage as they wish. In fact, I believe he would go further and state that it is none of our business how people 100 years from now want to define marriage. 
"On every question of construction (of the Constitution) let us carry ourselves back to the time when the Constitution was adopted, recollect the spirit of the debates, and instead of trying what meaning may be squeezed out of the text, or invented against it, conform to the probable one in which it was passed."
So I guess you've decided to try to debate Thomas Jefferson?
You will look long and hard before you find any provision in the constitution that states that the judiciary has greater power than other branches to interpret the constitution.
The notion of "Greater" or "Lesser" is a matter of perspective depending upon what you consider to be important. The fact that congress controls the money seems to me to be a very great power. That congress can impeach members of the court seems to me to make them of a higher power than the courts. That the executive controls the army, means the nation can launch a war that nobody wants against states attempting to gain independence from what they regard as tyranny. Again, a very great power. In fact, it was the ultimate power, because the President was arresting legislators and threatening to arrest Judges.
So all in all, even with the courts doing judicial review (and you didn't really answer who better should do it or why) they are still a poor third in terms of the power they wield.
It only looks like a lot nowadays because of the supine indulgent nature of the other two branches of government. Earl Warren should have been impeached, and so should many of the post Roosevelt appointed judges. Congress was just unconcerned with these Judicial breaches, and the Presidency was under the delusion that respect for Unconstitutional rulings by the courts should be given.