According to our current understanding of physics, it is not possible for anything with mass to travel at or exceed the speed of light in a vacuum. The concept you mentioned, that space seems to push back on objects approaching the speed of light, is related to Einstein's theory of relativity.
Einstein's theory introduced the idea that space and time are interconnected in a four-dimensional fabric called spacetime. Objects with mass cause spacetime to curve, creating what we perceive as gravity. When you try to accelerate an object with mass, you need to provide energy to overcome the resistance of spacetime curvature.
As an object with mass approaches the speed of light, its relativistic mass increases, and it requires more and more energy to continue accelerating. The increase in mass is accompanied by a decrease in the object's ability to accelerate. It's as if spacetime resists the object's motion, making it harder and harder to increase its speed.
As the object approaches the speed of light, its relativistic mass becomes infinitely large, and an infinite amount of energy would be required to reach or exceed the speed of light. This is known as the mass-energy equivalence principle, famously expressed by the equation E=mc², where E represents energy, m represents mass, and c represents the speed of light.
In essence, it is not space itself pushing back on the object, but rather the fundamental nature of spacetime and the relationship between mass, energy, and the speed of light.