Text-to-speech (TTS) has been extensively studied for generating high-quality speech with textual inputs, playing a crucial role in various real-time applications. For real-world deployment, ensuring stable and timely generation in TTS models against minor input perturbations is of paramount importance. Therefore, evaluating the robustness of TTS models against such perturbations, commonly known as adversarial attacks, is highly desirable. In this paper, we propose TTSlow, a novel adversarial approach specifically tailored to slow down the speech generation process in TTS systems. To induce long TTS waiting time, we design novel efficiency-oriented adversarial loss to encourage endless generation process. TTSlow encompasses two attack strategies targeting both text inputs and speaker embedding. Specifically, we propose TTSlow-text, which utilizes a combination of homoglyphs-based and swap-based perturbations, along with TTSlow-spk, which employs a gradient optimization attack approach for speaker embedding. TTSlow serves as the first attack approach targeting a wide range of TTS models, including autoregressive and non-autoregressive TTS ones, thereby advancing exploration in audio security. Extensive experiments are conducted to evaluate the inference efficiency of TTS models, and in-depth analysis of generated speech intelligibility is performed using Gemini. The results demonstrate that TTSlow can effectively slow down two TTS models across three publicly available datasets. We are committed to releasing the source code upon acceptance, facilitating further research and benchmarking in this domain.