Neural operators (NOs) have recently emerged as powerful tools for learning mappings between infinite dimensional function spaces through data-driven training. Our interest focuses on understanding whether these techniques can effectively learn the evolution of complex dynamical systems, in particular stiff ionic models that are crucial for simulating excitable cell dynamics. These systems present significant challenges to these techniques due to their inherent stiffness and multiscale dynamics. A recent study explored the ability of NOs to learn the mapping from the applied current to the transmembrane potential of the Hodgkin-Huxley model. Building on this, our study extends this methodology to investigate whether Fourier Neural Operators (FNOs) can learn the complex dynamics of all the variables in multi-dimensional ionic models, rather than just the transmembrane potential. We demonstrate the effectiveness of this approach by accurately learning the dynamics of three ionic models of increasing dimensionality: the two-variable FitzHugh-Nagumo model, the four-variable Hodgkin-Huxley model, and the forty-one variable O’Hara-Rudy model, achieving relative L^2 test errors of about 0.8%, 2%, and 2%, respectively. To ensure the selection of near-optimal configurations for the FNO, we conducted automatic hyperparameter tuning under two scenarios: an unconstrained setting, where the number of trainable parameters is not limited, and a constrained case with a fixed number of trainable parameters. Both constrained and unconstrained architectures achieve comparable results in terms of accuracy across all the models considered. However, the unconstrained architecture required approximately half the number of training epochs to achieve similar accuracy. The successful application of FNOs to the challenging ORd model, with its numerous variables and complex dynamics, suggests their potential utility in investigating other operators arising from stiff ionic models. Such operators are of particular interest in personalized medicine, where efficient simulations of complex biological systems are essential. This work establishes FNOs as a promising tool for capturing and predicting the intricate behavior of ionic models, even in high-dimensional scenarios.