There is no doubt in my mind that a successful invasion is likely... Due to the fact that we are more vulnerable within. However, think of it like when we were at Afghanistan, even after we were there for several years, there were still many people whom hated us "The Invaders" and took action to harm us. I doubt it would happen though, due to the fact that it would cost way to much to fund such an invasion.
We need to look at the basic math. If the rest of the world invaded, they would have the majority. Although the US might be strong and have nuclear weapons, other countries do as well. One single country could not stand up to the power of the rest of the world.
No country could stand against every country if they attacked in unison however this seems highly improbable as there are plenty of treaties mad which prevent something like this from happening. This would not really end well and I see it ending with the world being destroyed and uninhabitable anymore because of all the nukes being released around the globe.
1. It is highly improbable that NATO would join this alliance to invade America.
2. Unless America loses permanent UN membership, it can veto any resolution condemning them.
3. The US is a GIGANTIC trade nation with TONS of allies, so this coalition to attack America would likely be invaded by West before the West joins in.
4. US military spending is more than the next 10 nations COMBINED.
5. Without trade between America and other nations, the global economy would likely collapse, especially Europe, who would already be skeptical of the attack, likely resulting in a Eat vs. West war, which the West would likely win.
6. We have nukes, so no sane nation would attack us.
7. Widespread Pro-American rebellions would probably take place.
Bottom Line: America just is too strong, has too big of an ally network, and could bring down the global economy in a single shot. (Oh, and they also have nukes)
If the rest of the world teamed up on America, we'd dakka them with nukes.
Considering that the US is a major market for a lot of international products, "the world" would be restricted to a group of fringe lunatics with no grasp of reality.
The end result would be a lot of the world withdrawing after the first quarter.