During the evening's festivities in Silas Marner, how much progress does Godfrey make in winning Nancy's approval?

In chapter XI the New Year's Eve festivities allow Godfrey an opportunity to dance and talk with Nancy in the hope of gaining her favor.

It is the holiday season, and as is the custom, there is the great party at the Red House on New Year's Eve. Miss Nancy Lammeter looks "bewitching" in her attire. When her carriage stops, she does not want Godfrey Cass to help her down because she has found him fickle. He may pay no attention to her for weeks, and then, suddenly, he will pay her no shortage of attention. Also, Miss Nancy thinks that Godfrey "lives a bad life."

As the guests enjoy their dinner, Mr. Kimble asks Nancy to save a dance for him. Hearing this request, Squire Cass urges the apothecary to give the young people "fair-play." He then looks at Godfrey and asks his son if he has requested a dance with Miss Nancy.  Godfrey "saw no course open" but to turn to Nancy and speak.

"No, I've not asked her yet, but I hope she'll consent—if somebody else hasn't been before me."
"No, no objections," said Nancy in a cold tone.

While Godfrey dances with Miss Lammeter, the skirt of her gown, which is a little longer in the back than in the front, falls under the heavy foot of the Squire, and some stitches at the waist of her gown tear. After exchanging whispers with her sister, Nancy tells Godfrey that she must sit down until Priscilla can attend to her dress. Feeling "happy and oblivious under the charm of the country dance with Nancy," Godfrey quickly leads her to an adjoining parlor. After Nancy apologizes for her unluckiness, Godfrey tells her that it is "ill-natured" of her to be sorry that she has danced with him. Nancy quickly explains that she did not mean to "say what's ill-natured at all," adding that one dance must not matter. Godfrey contradicts,

"You know that isn't true. You know one dance with you matters more to me than all the other pleasures in the world."

Startled by Godfrey's show of emotion, Nancy sits perfectly still. After this momentary pause, she tells Godfrey that she did not know that dancing with her was such a pleasure. "If it is true," she adds, "I don't wish to hear it." However, Godfrey pursues his thoughts as he perceives this opportunity of being alone with her. He tells her, "You might encourage me to be a better fellow" because he is miserable and she offers him no comfort.  

Godfrey then decides to quarrel with her, hoping to elicit some kind of emotion. Unfortunately, Priscilla enters the room, so Godfrey asks Nancy if she wants him to leave. "As you like," says Nancy. "Then I like to stay," replies Godfrey with "reckless determination to get as much of this joy as he could."