The current US armed forces are not at all of the same nature they were ten years ago or even five years ago. The improvement in morale, training and effectiveness over the last five years is something that is nearly unprecedented, so far as my study of history can see.
I don't know what you study for that, but the statistics of the the activities in Afghanistan or Iraq actually show that the US Army is far away from high effectivity. The reports are sounding more like the troops are often suffering from friction - Some people might even think, friendly fire is a US invention. Or that all efforts and good payment are not helping to keep the moral of the US soldiers high when deployed far away from home.
Of course, the US army is now more effective as in Vietnam... but that is no challenge.
I would, for the sake of the soldiers of your country, remember that you have not fought a regular army since 1991. The air strikes on Serbia not taken in account, which had been no show case of US superiority. You have no evidence, that the US army is fighting better in real combat situations as in training or against irregular troops.
I would say, that even Georgian troops would be a major challenge for US troops, unless you have a clear superiority. By effectivity alone, you won't win a battle and should not rely on it. You can't rely on special forces and veteran units alone - the bulk of your fighting units will be regular units.
Which brings us back to the "not being able to police inside the USA". Can you stop Russia on it's own soil? Likely not. Can you accept losing the lives of soldiers for a rebel country, which only appeared on your radar for a massive counterfeiting?
The USA have a huge club with their army. But I would say, they have neither the will to do use it nor the understanding where to use it. And it will not get better, as better equipment (as the last ten years show) is no replacement for deficits in training.
EDIT/PS: Carrier wings and strategic bombers are great when you want to attack immobile targets which can't defend themselves. But actually, the only weapon of real importance for the USA so far, was the Tomahawk - and other countries have similar equipment.