Rapid advances in material science and mobile technology bring the new generation of wearable electrocardiogram (ECG) sensing systems. In particular, sensing textiles have been widely used in cardiac monitoring due to its high flexibility and reusability. Unlike conventional gel electrodes, sensing textiles are non-adhesive, which provide comfortable and stress-free experience. However, the quality of textile-based ECG sensing is more sensitive to external factors (such as sensor placement and contact pressure). There is an urgent need to investigate how the quality of ECG sensing is influenced by these factors and improve the design of wearable textiles. In the literature, little has been reported on the sensitivity analysis of textile-based ECG sensing. In this study, we experimentally investigate the sensitivity of textile-based ECG sensing to four factors, i.e., contact pressure, textile placement, user's activity, and muscle activity. Specifically, ECG signals are collected using sensing textiles under these four factors. Then, heart rate and ECG morphology are characterized from the obtained ECG signals and compared with true signals (obtained from standard gel electrodes). Experimental results show that the quality of textile-based ECG sensing is not sensitive to the contact pressure as long as it is >6N. When the patient is walking, nevertheless, the sensing quality can be strongly influenced by the textile placement. Furthermore, textiles placed on areas with fewer muscles achieve better signal quality. This study shows strong potentials of textile materials for the design of wearable ECG systems to empower smart and connected cardiac health.