Theoretically, yes, it could happen. Reality? Not likely. A military dictator might be able to take control of the federal government but it would be very difficult to take over the State governments without massive support. Of course, civilian firearm ownership makes this task even harder, which is the real reason behind the 2nd Amendment. We have the right to own firearms in this country for just this scenario. Any military take over of the government would be met with stiff resistance from a sizable portion of Americans.
Now, let's consider a plane crashing into the Capitol. How would that affect government? Not much really. Let's assume that the entire Congress was killed in the attack. Not really a big deal because the State legislatures would simply appoint interim Representatives and Senators until elections could be held. Should the President be killed then we would simply follow the line of succession going from the Vice President, Speaker of the House, President pro tempore of the Senate, and then on to the Secretaries of State, Treasury, Defense, Attorney General, Secretaries of the Interior, Agriculture, Commerce, Labor, Health and Human Services, HUD, Transportation, Energy, Education, Veterans Affairs and finally Homeland Security.
Now! Should ALL of those people and the Congress be killed off at the same time THEN we might have a problem. The chances of that happening are very slim. The only real scenario that would force that would be a nuclear attack in Washington DC. But then again the State Legislatures could appoint Reps and Senators who would then appoint an interim President and Vice President.
Would there be chaos? Sure. Would it be catastrophic? Indeed. Could it be handled? Yes, but it would be difficult. Is it plausible that the entire US government would be overthrown or even killed off? Yes! Likely? No.
Not only that but FEMA has contingencies plans for things such as this. Interesting to note that FEMA only spends 10% of its budget on natural disaster preparedness. The rest goes towards ensuring the survivability of the US government.