I don't know the official reason that Washington elites give when asked why they decided to call automatic budget cuts "sequestration" but it sure is ironic because one of the meanings of the verb form, "sequester," is to remove property from the possession of the owner temporarily until a lawsuit or other dispute is settled. Could it be that the federal government thinks that taxpayers' money is its own property so when a dispute over its use arises in Congress the funds have to be "sequestered?" A more interesting question is why Congress remains deadlocked over the budget. The simple answer is that a significant percentage of Americans, but by no means all, believe that the federal government has grown too big.
Are they right? Well, that (too) requires making a valuable judgement. But they certainly have empirical reasons to be concerned, as the time series chart above suggests. What it shows is that the U.S. government was first tiny compared to the overall size of the economy (Remember, the dispute between Hamilton and Jefferson was over whether the government would be tiny or teensy weeny, not "large" or "small" as reported in too many textbooks ... see my One Nation Under Debt for details.). During major wars (1812, Civil, WWI, WWII, all clearly visible on the graph), federal expenditures grew as a percentage of GDP, only to subside after the war. (Note, though, that they never went back to their prewar level. This is what economist Bob Higgs has called the ratchet effect.) Since the Depression, however, government expenditures/GDP have trended upward, first due to the New Deal, then to a series of minor "wars" (Korea, Vietnam, Cold, Drugs, Terrorism) and "races" (space, missile).
The growth of federal spending as a percentage of GDP was not monotonic after World War II but rather exhibited ups and downs with a clear upward trend that was not attenuated until the 1970s and partially reversed in the 1990s. (It wasn't that the government shrank -- nominal expenditures have grown every year but one since 1956 -- but rather that the economy grew faster than government expenditures under Clinton.) Since Obama has taken office, however, government expenditures have surged while the economy has been stagnant. Expenditures over GDP is therefore at a peacetime high.
Americans might be quite happy to allow government expenditures to continue to expand faster than the economy if they believed that they benefited from it in a significant way. Most don't, however, as evidenced by the dismally low approval ratings for Congress and other federal institutions, like Social Security (which people like when it is paying them or relatives but despise when its Fubar characteristics are explained).
The best of all worlds would be for Congress to increase the government's efficiency, to have it do what it currently does well with fewer resources and to have it stop doing things it does not/cannot do well. That is not going to happen, however, because few in Congress have the requisite brainpower and none have the necessary incentives to make such decisions.
Second best will be to suffer the sequestration cuts, skimp through the growth slowdown/recession likely to follow, and prepare for the economic boom likely to begin a year or two out.
Worse will be for Congress to "kick the can down the road" yet again (enact more temporary measures). The worst measure would be for Congress to continue to force huge deficits down the throats of our children, grandchildren, and great grandchildren.