Research on the factors influencing the acceptance of GenAI in language learning has expanded widely; however, few studies have focused on the role of language learning emotions. To enhance the effectiveness of GenAI-powered English-speaking instruction and the learning experience, this study expands on the Integrated Model of Technology Acceptance (IMTA) by investigating the role of various emotions and willingness to communicate in different contexts as intrinsic motivators for the acceptance of GenAI-powered conversational chatbots. Using a questionnaire (n = 368) and pre- and post-tests, the study found that EFL learners with higher communicative confidence and greater foreign language learning boredom tend to perceive GenAI chatbots as less useful for developing speaking skills. While GenAI successfully aided them in improving their speaking skills through both theme-based and free dialogues, learners who are more willing to engage in face-to-face interactions with peers and teachers may not find chatbots as productive or engaging as human counterparts. The results suggest that EFL teachers should be aware of the limitations of GenAI and students' individual differences, integrating GenAI into their classrooms in a way that aligns with student's proficiency and preferences to create a harmonious and efficient GenAI-supported language learning environment. This also underscores the importance of developing teachers' AI competence in the GenAI era.