No, it is not theoretically possible to liquefy helium at room temperature, regardless of the pressure applied. Helium is known as a "cryogenic" substance because it remains in its gaseous state even at extremely low temperatures.
Helium is unique among the elements because it exhibits what is called "zero-point energy." At absolute zero temperature (-273.15 degrees Celsius or 0 Kelvin), helium still possesses kinetic energy due to quantum mechanical effects. This residual energy prevents helium from condensing into a liquid state, no matter how high the pressure is.
To liquefy helium, it must be cooled to temperatures close to absolute zero. At normal atmospheric pressure, helium only liquefies below its boiling point of -268.93 degrees Celsius (-452 degrees Fahrenheit) which is just a few degrees above absolute zero.
At very high pressures, such as those found in the deep interiors of gas giant planets like Jupiter, helium can potentially exist in a dense metallic state. However, this state is distinct from a conventional liquid and is only achievable under extreme conditions of pressure and temperature found in planetary interiors.
In summary, due to the peculiar quantum properties of helium, it cannot be liquefied at room temperature or even at high pressures. It requires very low temperatures close to absolute zero to transition from a gas to a liquid state.