- American airspace only
- Supply available for long flight
- air refuelling possible
- threat from enemy forces on the ground.
- No international assistance
A realistic period of time that Air Force One can stay in the air.
Problems I see:
the isolation of the occupants
Air Force One is a military aircraft in a permanent stress situation with ( supposed to be ) strict hirachy, however the pilot has the final say on the flight and doctors can write military unfit for duty.
Food and water
Air Force One can serve up to 300 meals at a time however it can also transport over 100 people. So it's difficult to say how much supply is on board.
And on long journeys without access to fresh fruit, scurvy can be a problem. It depends on the vitamin tablets on board.
Basically the same as food and water, no indication of how large the medical reseven is, just that there is an operating room on board. However, there was/is a map of Air Force One for rescue councils on the internet showing the oxygen tank and other details. Maybe one can estimate the supplies with that.
The Air Force One is thoroughly checked before every take-off, however no aircraft is designed to fly for weeks on end. There are certainly parts that will fail after days (weeks ?). However, I don't know much about this and if you don't have a time frame mapped out, by hand-waving after 3 weeks a major part will break.
The Vac-25 was being prepared for a long flight for President Eddie from Washington to Israel. Shortly after take-off, a military push proclaimed the United States of America 2.0 (now with 10% more weapons and freedom). This makes 95% of all military installations hostile to Air Force One. Only a few Air Force bases, spread across the country, are still loyal to the President on board Air Force One (mainly because pilot Bruce D. has a legendary reputation as a musician) and want to help him respectively the President. To this end, they try to regularly supply Air Force One with fuel by air refuelling.
Air Force One cannot hope for international help, as the President has angered the governments of almost the entire world through some "misadventures". And that several times.
However, the new government wants President Eddie alive to condemn him as a symbol of the old and have a clean break so they can start anew. To do this, they pursue Air Force One at a safe distance with their own jets and try to stop the attempts to supply Air Force One so that the plane has to land and the President can be arrested. On the ground, several intervention troops are ready if this happens. Air Force One itself is not attacked.
Bonus points: Is this situation considered a siege ?