Percy himself could be the one to resist. Despite all his adventures and his status as a powerful demigod, Percy has always had a strong sense of his mortal side. His love for his mother, his friends, and his experiences in the mortal world are very important to him. He has seen the flaws in the gods and might not want to become like them. He might worry about losing his sense of self and his ability to relate to mortals. Also, he has always fought against the idea of being controlled by fate or the will of the gods, and becoming a god would seem like giving in to that very system he has been fighting against.
Grover might be the most likely to resist. He has always been very connected to the mortal and natural world. His role as a satyr has been to protect and guide demigods in the mortal world. Becoming a god would mean leaving behind his familiar role and the simple joys of the natural world he loves so much. He might fear losing his identity and his close connection to the forests, meadows, and the young demigods he has befriended over the years.
I think Annabeth would be a strong candidate for resistance. She is highly intelligent and rational. She might question the implications and responsibilities that come with godhood. Annabeth has always been about using her knowledge and skills to build and protect in the mortal realm. Becoming a god would bring a whole new set of rules and politics that she may not want to be a part of. Also, she values her relationships with mortals, like her family and the other demigods, and being a god could potentially create a distance between her and them.