If, in 1860, an armed gang had broken into the Capitol during James Buchanan's last State of the Union message and shot him, all the senators and representatives, and all the Supreme Court justices, and then disappeared, what would the result have been?
My guess is anarchy.
That's not to say there would have been no government. The states would have held special elections to replace the dead representatives and the legislatures would have appointed new senators. There might have been elections held for a new president, but since the regular elections were only a few months away, I think Congress would have appointed a president pro tempore.
What I mean by anarchy is that even without a federal government to head things up, life in the areas that count—family, church, commerce—would have gone on unchanged. The farmers would have planted exactly what they would have planted anyway. The dairymen would take their milk, cheese, and butter to market the same as they had the year before. The churches and schools would have aired their grief at the slaughter and gone on with their affairs. People would still have traveled as freely as their finances allowed.
Not all would have been wonderful, of course. The slaves would still have been slaves—state governments are still governments, and some of them were essential supports for the slave system—but perhaps some northern states would have seceded out of revulsion against federal laws requiring fugitive slaves to be returned to their masters, and some southern states would have seceded to avoid tariffs. Pennsylvania would still have been a state on a par with the states of Great Britain and France.
The most common dealing most people had with the federal government was with the Post Office, and that would not have changed. Life would have continued on decently and in order.
What would happen if the president, Congress, and the Supreme Court disappeared tomorrow?
My guess is chaos.
There would be an immediate declaration of martial law, even if all credible evidence showed that the mayhem was spent. All citizens would be required to show identification and subject to random searches. Rationing and wage and price controls would be instituted, with the consequent black markets and violent turf wars. This would "necessitate," in the interests of security of course, that travel be restricted, and travelers and commuters would have to justify every movement. Dissent would be silenced, and all criticism of government policies would be taken as sedition.
Aleksandr Solzhenitsyn once watched youths crowd around and jeer a small congregation of elderly Orthodox Christians as they went about their Easter liturgy and asked something like, "Is this the new man the Revolution promised us?" We've saved the Union, reconstructed the South, had the progress of Teddy Roosevelt, made the world safe for democracy with Wilson, been given the New Deal by FDR, and implemented Johnson's Great Society, Reaganomics, the Contract with America, and now the Audacity of Hope. As a result, we're nothing like eagles, symbol of independence, who (in the Bible anyway) renew their strength by waiting on the Lord. We're more like the helpless, dependent little birds on the Louisiana flag.
I think that was the plan all along.