Theoretically it is possible. However, there are a couple of thing that get in the way. First of all, VTOL jets are harder to fly. This is one of the things that caused problems in the early days of the Harier fighter was getting the pilots properly trained to transition between horizontal and vertical flight. I suppoes that this transition would be even more difficult for a larger jet. The other problem is in fuel consumption. Vertical take off and landing burn up a lot of fuel. The bigger the plain, the more of a problem this would be. So, the economic costs involved probably out weigh the benifits for large planes.

Another big issue for VTOL (vertical take off and landing) as opposed to STOVL (Short take off, vertical landing), is engine thrust v's weight. In order to take off vertically you must have more combined engine thrust than weight. Harriers cannot take off vertically when fully loaded - their weight exceeds the thrust of their engine. Instead, they take a short run-up and then used vetical thrust to assist lift-off, or they use a short runway with a ramp at the end to launch into the air. With most commercial aircraft weighing in at over 100 tonnes fully laden, you would need very powerful engines to lift off vertically. As an example, the 747 weighs several hundred tonnes, but the engines they've had up until recently only put out about 25 tonnes of thrust each (about 54,000 pounds of thrust). It's plenty for horizontal propulsion, but nowhere near enough for vertical. The most powerful jet engine I'm aware of at the moment are the Rolls Royce Trent turbofans. The Trent 900 series were somewhere up around 100,000 pounds of thrust (about 45,000kg). I believe these engines will be used to power the Airbus A380. Another big issue would be structural design. Only one V/STOL aircraft that I know of has its propulsion outside its body - the V-22 Osprey. Most V/STOL (Vertical or short take off and landing) aircraft have their engines and propulsion nozzles in the body of the aircraft. An aircraft with pod mounted jet engines, as most commercial aircraft are, would put enormous strain on the structure of the wings if they had vertical thrust. You would also need to add maneuvring jets for the nose and tail and wingtips to give directional control during vertical thrust operation.

the engine would be much bigger than the airplane itself

Economically it is currently impossible. I did read one time years ago someone was thinking of circular runways that were banked allowing the aircraft to land and take off in a much smaller area. Guess it didn't work out as I have never seen a circular runway. I think it was in Popular Science Mag. in the 1960s