Accurate prediction of Length of Stay (LOS) in hospitals is crucial for improving healthcare services, resource management, and cost efficiency. This paper presents StayLTC, a multimodal deep learning framework developed to forecast real-time hospital LOS using Liquid Time-Constant Networks (LTCs). LTCs, with their continuous-time recurrent dynamics, are evaluated against traditional models using structured data from Electronic Health Records (EHRs) and clinical notes. Our evaluation, conducted on the MIMIC-III dataset, demonstrated that LTCs significantly outperform most of the other time series models, offering enhanced accuracy, robustness, and efficiency in resource utilization. Additionally, LTCs demonstrate a comparable performance in LOS prediction compared to time series large language models, while requiring significantly less computational power and memory, underscoring their potential to advance Natural Language Processing (NLP) tasks in healthcare.