While Prof. Auerbach's explanation seems consistent with Shabbos (88a) it is not the traditional view. There are a number of explanations offered in the classic sources. This post will be limited to the view that it is related to the difference between the Written and Oral Torah. I will present the other views in a future post.
1) The earliest source to address this issue is the Tanchuma (Noach #3) which differentiates between the Written Torah - which was accepted willingly and the Oral Torah - which required force to be accepted.
Tanchuma( Noach 3): The Jews did not accept the Torah until G‑d forced them by threatening them with the mountain held over their heads as it says (Shemos 19:17): And they were camped under the mountain. R’ Dimi bar Chama said that G‑d told the Jews that if they would accept the Torah then it will be good and if not they would be buried there (Shabbos 88a). However this raises the question. If they were forced to accept the Written Torah then why when they were asked if they wanted to accept the Torah they all answered na’aseh v’nishma (we will do and then we will understand). We can answer that there is no effort or strain in the Written Torah and it is not very large either. Therefore they readily accepted the Written Torah by saying na’aseh v’nishma but they were forced to accept the Oral Torah which has much detail both for the minor mitzvos and the major mitzvos and there is a great quantity as well. The Oral Torah presents great difficulties and no one would study it except someone who strongly loves G‑d with his full heart and with his entire soul and with all his might…
2) The Maharal objects to a literal understanding of this medrash
Maharal (Ohr Chadash): Tanchuma (Noach #3) asks why G‑d had to force the Jews to accept the Torah by holding Sinai over their head when it says in Shemos (24:7) that the Jews willing accepted the Torah by saying na’aseh v’nishma (we will do and then understand)? The Tanchuma answers that they only willing accepted the Written Torah and not the Oral Torah because the Oral Torah has many difficult details and therefore they had to be forced to accept the Oral Torah. However this explanation is also problematic in saying that in reality the Jews did not want to accept the Oral Torah. It doesn’t make sense that they did not want the full merit of the Torah whether it was the Oral or Written Torah. It would appear that the explanation is that they did not want to accept the Oral Torah until they were forced. That is because it is appropriate to be forced for the Oral Torah. In contrast the Written Torah which is the beginning of the process of acceptance of the Torah needs to be totally voluntary since the Jews were essential prepared to accept the Torah and thus it wasn’t relevant that they should be forced nor was it necessary. In contrast, the Oral Torah is not such a natural thing to accept as the Written Torah which is the basis to all the Torah. The Jews were inherently ready to accept the Torah and the Written Torah is Torah so the force was only needed for the Oral Torah. However it is not correct to say that the Jews did not want the Oral Torah and that therefore it was necessary to force them and reduce the merit of the Jews. Rather the Tanchuma is say that everything was done in the appropriate manner. The difficulty addressed by the Tanchuma is that it seems that na’aseh v’nishma was the acceptance of both the Written and Oral Torah and therefore there was no need for the forced acceptance. The answer is that na’aseh v’nishma was not in fact said concerning the Oral Torah which is much more difficult. Therefore the acceptance of the Written Torah and Oral Torah was distinct and separate from each other and each one was accepted in the appropriate manner. When you understand the words of our Sages in their full truth you will understand that this explanation which we have given is the essential one and this is clear…
3) However the Ohr HaChaim presents a similar understanding to the medrash - without actually citing it.
Ohr HaChaim (Shemos 19:5): The reason for the repeated verb of listening in this verse perhaps alludes to the acceptance of the two types of Torah. The first being the Written Torah which they received at Sinai and the second being the Oral Torah and the dikdukei sofrim and seforim as well as the legistaltion which would be taught by the rabbis in the future. This is hinted at by the mitzva of lo sassur (Devarim 17:11)…. Furthermore the verse mentions “My voice” after this double expression. This alludes to the principle mentioned in the Bamidbar Rabbah (14): “That which is heard from a sage has the same authority as hearing something from G‑d.” In other words, those decrees of the sages have the same authority as if they had been said by G‑d. Perhaps this insight that they were actually accepting two types of Torah at Sinai can explain a difficulty in understanding Shabbos (88a). This gemora understands the verse Shemos 19:17) to mean that G‑d forced them to accept the Torah by threatening to kill the Jews by holding Mt. Sinai over their heads - unless they accepted the Torah. The obvious problem with this interpretation is that Shemos (24:7) says that they accepted the Torah willingly – naaseh v’nishma (whatever G‑d says we will do and afterwards will learn). In view of their ready acceptance why was it necessary to force them?… It is possible to answer this question with our explanation – that they in fact accepted two types of Torah at Sinai one directly from G‑d at Sinai and a second one that they would receive in the future from the sages. Their willing acceptance described in Shemos (24:7) was the acceptance of what they heard from G‑d even before they knew what it entailed. In contrast the Torah which they would be taught in the future by the sages they refused to accept before they heard what it contained. Their objection to accepting it was that the Torah of the sage is unlimited and in each generation new laws and decrees are generated. Thus G‑d had to force them to accept the Oral Torah while the Written Torah was accepted willingly. This forced state of acceptance continued until the time of Mordechai when they saw the importance of the sage through the actions of Mordechai and Esther. They saw that without their actions there would not be any remnant left of the Jewish people because of their enemies. At that time they also willingly accepted the Torah of the Sage. However it must be acknowledged that our sages (Shabbos 88a) understood the verse differently. They say that it indicates that the Jews willingly accepted the entire Torah willingly even before they knew its contents. Consequently they praised the Jews at Sinai as being like the angels who also accept obligation fully before knowing what it is. However this explanation of the sages is homiletics. According to our explanation they also said they would accept prior to understanding what it entailed – but we insist that was only the Written Torah that they heard directly from G‑d. In fact it might be possible to reconcile these two approaches by saying that these two explanations are describing two different types of Jews. Perhaps our sages are describing the total ready acceptance by the completely righteous Jew. We would then say that the resistance to accepting the Torah of the Sages only occurred amongst the masses. It is obvious that not all the Jews were on the same level of righteousness.
The distinction between the Written and Oral Torah is also found in many other sources. Here are are few more.
Rabbeinu Bachye (Shemos 19:8): All that G‑d said we will do. They agreed to accept upon themselves the yoke of Torah and mitzvos and they did this willingly. However this that our Sages say that Sinai was held over them like a barrel and that they were told that if they accepted the Torah it would be good but if not they would be buried there – it only was in reference to the Oral Torah. That is because the Oral Torah has many prohibitions and punishments as well as additional restrictions. In contrast they Written Torah was willingly accepted by everyone with great interest and joy as well as good heartedly. There was no need to apply force except for the Oral Torah.
Alshech(Bamidbar 21:14): G‑d came to give sight to the blind and to reject the view of the Jews who mistakenly think that the Oral Torah wasn’t necessary but only the Written Torah. In fact this mistaken view was that held by the Jews at Sinai. That is the reason it was necessary for G‑d to hold Sinai over their heads and to tell them if they accepted the Torah it would be good and if not they would die. The Tanchuma (Noach 3) asked that since they had already said na’aseh v’nishma (we will do and then we will understand) then why were they forced to accept the Torah under fear of death? And how could it be that there was no genuine acceptance until Purim? The Tanchuma answers that they fully accepted only the Written Torah and not the Oral Torah with its many details
Beis HaLevi(Mishlei 2:1): Shabbos (88a) says that because the Jews were forced to accept the Torah they had an excuse for why they shouldn’t be punished for sins. Nevertheless they fully accepted the Torah in the time of Achashveros… Tosfos (Shabbos 88a) asks why was it necessary to force them since they had already said na’aseh v’nishma (we will do and then we will understand)? The commentaries have already explained the main reason for forcing their acceptance only concerned the Oral Torah. In other words that they should accept doing all that they would be taught by the rabbis in every generation. Thus their original acceptances was only for that which G‑d had already said. They had to be forced to accept that which the rabbis would teach in the future.
Haflaah(Kesubos – Introduction #3): …Because without the Oral Torah we would not know what to do even concerning a single mitzvah… And many commentaries write that the main reason for threatening them with the mountain if they didn’t accept the Torah – only applies to Oral Torah. In fact that is the reason that Korach was swallowed alive in the earth because he rejected Moshe who represented the Oral Torah. Consequently he perverted the foundation principles of Judaism. For example he asked whether a talis which was dyed with techeles required a blue thread in the corner. …
Rav Tzadok(Machshavos Charutz #17): And when prophecy departed - It appears to me that this was the result of the increased power of intellect associated with the Oral Torah after they accepted the Torah a second time during the days of Achashveros because of the love associated with the miracle. They accepted the Torah then strongly and passionately. That was because originally the forced acceptance concerned only the Oral Torah because of the great effort involved in extracting Torah through the intellect and in ascertaining the truth. This understanding is stated in the Tanchuma (Noach #3). However after the events of Purim they willingly accepted the struggle and toil connected with the Oral Torah and by means of this merited the prophecy of intellectual wisdom. This enabled them to know everything by means of the ruach hakodesh which was in their hearts [and therefore they didn’t need the traditional prophecy].