What is Sankara's reply to this argument?
What the Vedas state need not necessarily serve the purpose of involving us in any work. The mimamsakas accept the Vedas because, according to them, the karma mentioned in them serves a purpose. So the purpose served by karma is the message of the Vedas, not the karma itself. If to be without any karma, without any work, is itself a great purpose, must not the jnanakanda of the Vedas then be acceptable since it deals with a condition in which there is no karma to be performed, or nothing is to be done? That is if being without karma is "useful" by itself - if it serves a "purpose" - that can also then be the message of the Vedas. So the underlying goal of the Vedas is not karma itself but the purpose behind it.
The Vedas admonish us: "Do not drink wine". How do we react to this interdiction? We react by doing nothing; there is indeed nothing for us to do. The message of this Vedic commandment is that we ought not to ruin ourselves by drinking. To remain without doing anything is called "abhava". All nisedha (prohibition) belongs to the abhava category. The mimasakas themselves admit that the Vedas forbid certain actions. If it is beneficial not to perform certain actions, how can you object to the possibility that not doing any karma at all can also constitute a great purpose? Vedanta has great "use" thus since it serves the supreme purpose of the action-less or quiescent state in which we realise the Self. This cannot be rejected as arthavada.
Krsna says in the Gita: "Sarvan karma' khilam Partha jnane parisamapyate" (All works, Partha, find their goal in jnana). All karma must be consecrated to Paramesvara, must be laid at the feet of the Supreme Lord. To be without work, and experience the bliss of the Brahman is he greatest of "uses". In this state there is no birth again and it means freedom from worldly existence. That is the ultimate message of the Vedas. The karmakanda must be woven together with the jnanakanda if it is to be meaningful and if it is to serve a purpose.
Sankara succeeded in convincing Mandanamisra, Kumarilabhatta and others about the rightness of this view. To recapitulate his argument: "The karmakanda of the Vedas mentions works because their performance is of some use in cleansing the mind. If the purpose achieved by not performing them is a million - million times greater than that gained by performing them, then that must be understood to be the message of the Vedas, the ultimate teaching of the jnanakanda. The karmakanda helps a seeker in his early stages. The performance of rites creates inner purity and takes him to Isvara. Karma performed for the sake of karma leads a man nowhere. The Vedas speak of the sannyasin's stage of life in which the ascetic, as he attains the Paramatman, becomes the Paramatman". The Acarya spoke in this vein to Mandanamisra [converted him to his point of view] and gave him initiation into sannyasa.
In the karmakanda certain acts are declared sinful. If a person keeps doing them it is because he feels he finds some pleasure in them. But such pleasure is momentary and becomes an obstacle in his efforts to know the joy that is greater. The mimamsakas, respecting the injunctions of the Vedas, abjure sinful acts. By the performance of Vedic karma they derive certain fruits, a certain degree of happiness, find well-being in their mundane existence and go to the pitr-loka or devaloka. But these do not mean everlasting bliss. When the fruits of their virtuous acts are exhausted, the joys also come to an end. Even if they go to the world of the celestials they will have to plunge into this world again on exhausting their merit. "Ksine punye martyalokam visanti".
What is that well-being which is eternal? The answer is that which is experienced by the jnanin when he dissolves in the Supreme Godhead. Then there is no "doing" for him. One must abjure sinful acts that afford petty momentary pleasure and instead perform noble works such as those mentioned in the Vedas. But what use are even these if they do not lead to the experience of plenary bliss? Are we, however, capable of directly attaining such blessedness abandoning Vedic karma? No. Jnana is not easy to obtain. For it the consciousness, the mind, must be made pure and un-oscillating. So Vedic rituals are essential.
But they must be performed not for impermanent rewards like paradise but for the removal of inner impurities. We must not be deflected from the higher path by the fruits yielded by karma- these must be placed devotedly at the feet of the Lord. He will bless us with the higher fruit of inner purity and then the mind will become mellow enough for Atmic inquiry, for the inward journey. That is the way to the supreme blessedness, the quiescent state in which one is oneself.
For a general background, please see here