One such proponent of this claim was a Reformed apologist and professor, Dr R. Scott Clark, on his blog (Here). Though Clark puts special emphasis on Calvin's use of the phrase "whole course of his obedience," and "whole life of Christ," and "obedience that he manifested in his life," I think Clark is unwittingly putting words into Calvin's mouth and committing a word-concept fallacy. In short, Clark mistakenly thinks that just because Calvin uses the term "obedience," including modifiers such as "whole" and "life," that Calvin must be speaking of Christ's "active obedience" (so called).
To further buttress his argument, Clark plainly admits (in the comments section) that:
What is essential here is that Christ did not come to qualify himself to be a Savior. Note how Calvin treated Christ’s obedience as if it were for us (that’s a crucial Protestant theme) not for himself. Those who denied IAO typically (following Anselm) assume that Christ owed obedience for himself, in order to qualify himself to be a Savior on the cross. This wasn’t the framework within which Calvin interpreted Christ’s life and death.Basically, Clark denies this "obedience" prior to Good Friday was dealing with Christ having to "qualify" as a worthy and spotless Sacrificial Lamb, and Clark even claims Calvin denied this as well.
Given this, I think it's important to look at the Calvin quote ourselves, but since it is so long I will only quote portions of it (with my own emphasis and highlights).
When it is asked then how Christ, by abolishing sin, removed the enmity between God and us, and purchased a righteousness which made him favourable and kind to us, it may be answered generally, that he accomplished this by the whole course of his obedience. This is proved by the testimony of Paul, “As by one man’s disobedience many were made sinners, so by the obedience of one shall many be made righteous,” (Rom. 5:19). And indeed he elsewhere extends the ground of pardon which exempts from the curse of the law to the whole life of Christ, “When the fulness of the time was come, God sent forth his Son, made of a woman, made under the law, to redeem them that were under the law,” (Gal. 4:4, 5). Thus even at his baptism he declared that a part of righteousness was fulfilled [Mt 3:15] by his yielding obedience to the command of the Father. In short, from the moment when he assumed the form of a servant, he began, in order to redeem us, to pay the price of deliverance. Scripture, however, the more certainly to define the mode of salvation, ascribes it peculiarly and specially to the death of Christ. ... [Calvin then quotes various passages of Scripture, Mt. 20:28; Rom. 4:25; John 1:29; Rom. 3:25; Rom. 5:9; 2 Cor. 5:21] ... In the Confession of Faith, called the Apostles’ Creed, the transition is admirably made from the birth of Christ to his death and resurrection, in which the completion of a perfect salvation consists. Still there is no exclusion of the other part of obedience which he performed in life. Thus Paul comprehends, from the beginning even to the end, his having assumed the form of a servant, humbled himself, and become obedient to death, even the death of the cross (Phil. 2:7). And, indeed, the first step in obedience was his voluntary subjection; for the sacrifice would have been unavailing to justification if not offered spontaneously. Hence our Lord, after testifying, “I lay down my life for the sheep,” distinctly adds, “No man taketh it from me,” (John 10:15, 18). ... We must bear in minds that Christ could not duly propitiate God without renouncing his own feelings and subjecting himself entirely to his Father’s will. To this effect the Apostle appositely quotes a passage from the Psalms, “Lo, I come (in the volume of the book it is written of me) to do thy will, O God,” (Heb. 10:5; Ps. 40:7, 8). Thus, as trembling consciences find no rest without sacrifice and ablution by which sins are expiated, we are properly directed thither, the source of our life being placed in the death of Christ. ... He therefore suffered under Pontius Pilate, being thus, by the formal sentence of the judge, ranked among criminals, and yet he is declared innocent by the same judge, when he affirms that he finds no cause of death in him. Our acquittal is in this that the guilt which made us liable to punishment was transferred to the head of the Son of God (Is. 53:12). We must specially remember this substitution in order that we may not be all our lives in trepidation and anxiety, as if the just vengeance which the Son of God transferred to himself, were still impending over us.When examining this quote, the first thing to keep in mind is that throughout all this, Calvin is commenting, line by line, on the Apostles' Creed. In the section Clark quoted, Calvin was focused upon the part of the Creed relating to Christ's birth, suffering under Pilate, and death. Notice how nothing in the Creed comes anywhere close to advocating "active obedience."
With that in mind, you'll notice how Calvin is exclusively focused on Christ's suffering in all this, nothing about "keeping the Law in our place," consigning his use of "obedience" entirely to Christ's suffering. All Calvin is saying is that Christ's suffering for us began at His birth.
The next thing to realize is that Calvin quoted many famous alleged "active obedience" proof texts from Scripture (which I highlighted in bold), notably Rom 5:19, Gal 4:4-5, Mat 3:15, and 2 Cor 5:21, yet Calvin clearly isn't interpreting them in terms of "active obedience"!
The final thing to take note of is that Calvin explicitly says, "the first step in obedience was his voluntary subjection; for the sacrifice would have been unavailing to justification if not offered spontaneously" and a bit later, "We must bear in minds that Christ could not duly propitiate God without renouncing his own feelings and subjecting himself entirely to his Father’s will." What Calvin explicitly affirms here is precisely what Clark explicitly denied Calvin (and Reformed) as teaching: that Christ's obedience prior to the Cross was precisely to qualify Him as a worthy Sacrifice.
I'd say the lesson to take away from this is twofold. First, that Dr Clark didn't accurately represent Calvin's view and words on Christ's obedience (which Calvin limited to passive obedience only), at least not in this quote. Second, that if Calvin truly believed in "active obedience," which is so critical to Reformed theology, then surely he'd have spoken clearly about this ultra critical concept elsewhere in his Institutes (which folks like Clark could then readily quote from).