Can't spend time on station? Seriously?
There is a reason that aircraft carriers are the first choice for applying force when long-term force is required.
I've spent six months at a time tooling around in the Arabian Sea. I know of at least one year-long cruise by the Nimitz where they spent about 5 days in-port (crew relief was the only reason they went off station). American aircraft carriers are refueled, rearmed, and resupplied by a massive fleet of auxiliary stores vessels capable of delivering anything, including an entire fighter (granted, I only saw the fighter thing happen once), fuel, munitions, stores, spares, and personnel. The only reason that an undamaged (combat or in-service events: fire/accident, collision, storm) carrier needs to be rotated off station is for crew relief. A carrier is quite capable of sailing for years at a stretch without docking. It's not practical, though, since the crew would be batshit crazy by then. But that's why we have plenty of them.
The actual operating expenses attributed to a fleet at sea is a moot. Those ships, crews, and aircraft would be sailing/flying somewhere, in any event. The additional expenses attributed to combat operations are identical no matter where the aircraft are based. Fuel to fly, munitions to deliver. Those would be present no matter the situation.
Day-long inter-continental missions (for one-offs or small-scale ops) are fine and actually better creating a nearby land base since that obviates the necessity of creating the required maintenance facilities (including the specialized (by aircraft type) maintenance equipment and supporting systems) as well as secure, sheltered bunkers for aircraft and facilities for crew and support people. Those are major expenditures. Modern aircraft require sophisticated electronics that aren't repaired by simply tossing the box on an electronics bench and poking around with meters and scopes. Many systems require multi-million dollar automated testing systems that utilize computers to perform the actual testing and troubleshooting (not all of it, just the long dull portion). In some cases, flight data computers, for example, complete manual testing could take weeks, while the CAT systems can complete the same testing during a single shift (or so). In addition to the electronics, there is the matter of support equipment for the mechanical systems (electrical, engines, hydraulic), ground support equipment, specialized stands and racks to handle engines/fuselage sections/wings.
And that doesn't even touch on the personnel aspects. Housing for crews, maintenance teams, medical, support staff.
In essence, setting up an new land facility as opposed to using a existing carrier or mounting an inter-continental strike is too expensive.
As shown by your reply, you don't actually understand mechanics of airstrikes or the application of tactical/strategic air power from sea-based platforms. There are quite a few long-service vets on Slashdot who won't hesitate to pounce on uninformed comments.
tl;dr: It's no simple or inexpensive task to support aircraft in the field. Aircraft carriers can loiter and prosecute an action for longer than you'd be willing to stay at sea cooped up, seeing the same couple dozen people 24/7. Aircraft carriers or inter-continental strikes are usually the best way to proceed unless you're gearing up for a very long, very large forward action (think invading another country, not a NATO action like Kosovo).