The Ketav Sofer, in his commentary on the Torah, applies this to Jews who truly love Judaism, but reject the need to actually fulfill the commandments in their entirety. The focus is on the last part of the curse, "To do them." He describes a style of Jew that is quite common.
This person believes that the ethics and values in Judaism are wonderful. He, however, believes that many of the rituals and commandments are antiquated and, bluntly, often primitive. Of what value is refraining from driving on the Sabbath? What is the point of wrapping tefillin around my arm and head?
Ah, but social justice! That is important! This Jew claims to have internalized the ethics of Judaism, and reached the point where the actual fulfillment of rituals is unnecessary. He believes that Judaism came to civilize the world, and, therefore, we must fight for that social justice. This becomes his Torah, his commandment.
The Ketav Sofer applies this curse to that person. Had "Cursed is the one who shall not fulfill the words of this Torah," been the whole phrase, it might have implied that this man has merit. After all, he is fulfilling the words of the Torah in his heart, and in his pursuit of a better world. But the verse continues, "To do them," which includes the physical fulfillment of all of the commandments of the Torah. What this person fails to comprehend is that the physical fulfillment of the commandments is necessary to create that better world.
It can be compared to a person who has a problem with being overweight. To go into the clothing store, buy clothing a few sizes too small, and start behaving like a thin person will do nothing to solve the problem. Only diet and exercise. Why? Because excess weight is not a psychological or sociological problem. It is a physical one. We humans are a magical combination of the physical and spiritual being. Man requires control of his physical self, just as he requires control of the spiritual self. We need to accept the spiritual Torah together with the physical commandments.
Thus, the second aspect of our lives to strengthen in preparation for Rosh Hashanah is our physical fulfillment of the commandments, "to do them.". Here comes the third.
The Ramban, in his commentary on the Torah, quotes the Jerusalem Talmud in interpreting this curse quite literally. "It is the Sexton," according to the Jerusalem Talmud, who was being cursed. The Ramban explains that it refers to the person responsible for placing the Torah scrolls safely in their ark. Should they be placed carelessly, they might fall. Alternately, the Ramban suggests that it refers to one who refuses to fulfill the function of Hagbaha, or the lifting and showing of the Torah scroll to the congregation.
According to these applications, the proper translation of the verse is, "Cursed is the one who will not lift up (literally) the words of this Torah…" The Ramban, however, sees this explanation as a parable for a much deeper problem.
There have been many pious Jews who may have run afoul of this curse. How so? Because they failed to broadcast and influence others with their piety. One who has the ability to strengthen the Torah amongst the Jewish people and fails to do so, no matter how personally observant he is, has not lifted up or caused to be fulfilled the words of the Torah. When one lifts the Torah scroll to show it to the congregation, one is sharing that Torah with others. That is the imperative learned out from this curse.
Those Jews who disconnect from their nonobservant, partially observant or observant in non-Orthodox ways brethren, are missing the point of their Judaism. Perhaps the greatest commandment of our time is the commandment to help reconnect Jews to their tradition and to observance.
Thus, after listening and doing, comes the third preparation for the High Holidays: reach out and share your Judaism. Every synagogue must prepare to welcome worshipers who only show up at this season. Torah is on display, it is our task to lift it up as high as we can and show it to the whole world. Blessed is the one will lift up, fulfill, and inspire all of Israel with the words of this Torah, in order that they may be fulfilled both spiritually and physically.
This is as we say the daily prayers, "Put it in our hearts to understand, to getting knowledge of, to listen, learn and teach, guard, do, and sustain all words of Your Torah with love."