It is called a tug. The tower is where the controllers hang out.
The ones we used for normal size jets were still pretty hefty, big turbocharged diesel engines.
As has been said, it does depend on the surface and most airports are fairly flat areas. A 17 year old high school student and I moved a 4engine Lockheed Jetstar once, by pushing on the main gear tires to get them rolling. It was very slightly downhill. The pilot manned the brakes. On the same ramp I once pushed a Lockheed Electra around with a half-ton pickup. It is wise to remember that brakes are as important as the ability to get it moving.
Happiness is not seeing another trite Ste. Maarten photo all week long.