Text-to-image diffusion models (SD) exhibit significant advancements while requiring extensive computational resources. Existing acceleration methods usually require extensive training and are not universally applicable. LCM-LoRA, trainable once for diverse models, offers universality but rarely considers ensuring the consistency of generated content before and after acceleration. This paper proposes SpeedUpNet (SUN), an innovative acceleration module, to address the challenges of universality and consistency. Exploiting the role of cross-attention layers in U-Net for SD models, we introduce an adapter specifically designed for these layers, quantifying the offset in image generation caused by negative prompts relative to positive prompts. This learned offset demonstrates stability across a range of models, enhancing SUN's universality. To improve output consistency, we propose a Multi-Step Consistent (MSC) loss, which stabilizes the offset and ensures fidelity in accelerated content. Experiments on SD v1.5 show that SUN leads to an overall speedup of more than 10 times compared to the baseline 25-step DPM-solver++, and offers two extra advantages: (1) training-free integration into various fine-tuned Stable-Diffusion models and (2) state-of-the-art FIDs of the generated data set before and after acceleration guided by random combinations of positive and negative prompts.