If you want to see it on a small scale, well ask yourself why the US has been unable to secure Afghanistan or Iraq. They had considerably more forces than your silly "1 aircraft carrier" scenario, it was hardly the whole population fighting, yet after years and years, they have been unable to secure the countries.
Afghanistan and Iraq actually prove my point. A fraction of the US armed forces was able to install a new government in each country in very short time. Since then, the fact that the insurgents have weapons leads to a lot of suffering on both sides, but it does not threaten the power of the US-backed government.
There are quite a few examples of unarmed civilian uprisings that have lead to a change in government, but I can't think of a single armed civilian uprising that has overturned a government with an air force.