"I implored G-d at that time saying, ...". (Deuteronomy 3; 23). Rashi notes that the word for 'implored' (which gives us the name of the Torah portion), 'va'eschanan' always means asking for a free gift. He explains: Even though the righteous could ask G-d in the merit of their righteous actions, they only ask G-d to give them a free gift, for G-d has said "I will show favour to whom I chose" (Exodus 33; 9).
Rabbi Yonasan Eibschitz, in his work Tiferes Yehonasan explains that they are not asking for G-d to give them something for nothing, but rather that they pray for their request to be fulfilled in the merit of what they will be able to do through the granting of this petition. Similarly, the Talmud (Sota 14a) explains that Moshe's sole motivation for wanting to enter the Land of Israel was in order that he should be able to perform the Mitzvot that can only be kept there, such as terumah, ma'aser, and tithes for the poor.
The Talmud (Kidushin 30b) states: "A person's evil inclination grows stronger every day, and tries to kill him, And if G-d would not help him he would never be able to overcome it." Furthermore, the Mishna (Avot 2; 4) says: "Don't trust in yourself until the day of your death." This means that even the most righteous person cannot rely on the fact that they have not sinned as an assurance that they will not sin in the future. If so, how could Moshe pray to G-d in the merit of Mitzvot that he hopes to perform in the future? Without G-d's help he has no guarantees that he will be able to keep the Mitzvot.
Later in the Portion the Torah states (5; 26) "Who can assure that this heart should remain theirs to fear Me [G-d] and observe all My commandments all the days?" On this the Talmud (Avoda Zara 5a) comments: Moshe said to the Jews, 'You are ungrateful, the children of ungrateful people. When G-d asked "Who can assure ..." you should have replied, "You, G-d, guarantee it for us.".
The Chazon Ish asks, how could the Jews be expected to ask G-d to ensure that they not sin? Doesn't that negate the entire concept of free choice? He answers that G-d gives free choice to each person. However, a person is permitted to persuade his fellow to serve G-d, either through force, or through encouragement. This is not considered annulling their free choice, since the actions he performs through his own free choice, and all of Israel are considered as a single person. This is the meaning of the verse; who can assure that there will always be righteous people in each generation concerned with bringing the hearts of the people close to the service of G-d.
G-d does not normally place this closeness in a person's heart, because if He would it would not have come from the person. If, however, a person prays to G-d that they should be brought close, and their prayers are answered, then the closeness that G-d brings about is attributed to the person, since it came about through his prayers. This is the meaning of the statement in the Talmud, that the Jews should have asked G-d to give the assurance. In other words, through this G-d would have been able to bring them close, since it would have been through their prayers.
This is Moshe's prayer. "You have begun to show your servant Your greatness...". Until now Moshe's prayers to come close to serving G-d have been answered, and he has reached the highest level of attachment to G-d that it is possible for a human being to attain. He is now praying that G-d continue to help him to draw close to G-d, through performing the Mitzvot, and to give him a chance to perform even more Mitzvot by entering the Land of Israel. Moshe is not asking that G-d answer him based on his past performance, but is praying that he be given not only opportunities to fulfil more Mitzvot, but the personal capabilities and inner strength to rise to the challenge of his evil inclination, and continue to draw close to G-d.