1. Individual and States' Rights, Capitalism: Most vital and responsive services do not go through the federal government. With the exception of some federal employees, a federal government shutdown does not immediately interfere with the daily lives of most citizens.
Your mileage may vary based on which European nation(s) you relate best to, but the percentage of government employees in the U.S., while uncomfortably high, is roughly half that of Norway's (15.9% versus 30%), and the U.S. is at least a couple points below average when compared to the whole of Europe.
If Americans need to buy something, send something, or be somewhere, they rely largely on private commerce. When they need a bill made into law, a judgment passed on a matter in federal courts, a presidential pardon, a war declared, etc. they need Congress or the judiciary or the presidential office or investigative task forces up and running. Local law enforcement provides the bulk of peacekeeping services, and the division of responsibilities into state and local government and private commerce explains much of the resiliency. The grocery store, the gas station and the Internet still usually function just fine for the interim. This is designed into the Constitution, that the people and the states respectively reserve the broadest rights (Articles 11 and 12 in the original Bill of Rights).
The more federal shutdowns there are, the more the people and the states will be weaned off of the necessity for daily federal intervention in their personal lives.
It has been acceptable for Congress to convene only occasionally in the past, so why not today?
2. Federalism itself, leading to benefits of scale: A primary argument for the federal government advanced in the Federalist Papers was that the United States would be more robust to local commercial upset and to partisan intrigue:
It has often given me pleasure to observe that independent America was not composed of detached and distant territories, but that one connected, fertile, widespreading country was the portion of our western sons of liberty. Providence has in a particular manner blessed it with a variety of soils and productions, and watered it with innumerable streams, for the delight and accommodation of its inhabitants. A succession of navigable waters forms a kind of chain round its borders, as if to bind it together; while the most noble rivers in the world, running at convenient distances, present them with highways for the easy communication of friendly aids, and the mutual transportation and exchange of their various commodities.
With equal pleasure I have as often taken notice that Providence has been pleased to give this one connected country to one united people--a people descended from the same ancestors, speaking the same language, professing the same religion, attached to the same principles of government, very similar in their manners and customs, and who, by their joint counsels, arms, and efforts, fighting side by side throughout a long and bloody war, have nobly established general liberty and independence.
This country and this people seem to have been made for each other, and it appears as if it was the design of Providence, that an inheritance so proper and convenient for a band of brethren, united to each other by the strongest ties, should never be split into a number of unsocial, jealous, and alien sovereignties.
3. The ethics and values of the people themselves. The current implementation of Constitutional rights and federalism is far from perfect, but self-reliance is built into the very ethic of the people. To the extent that it still prevails, the unity and solidarity of the American people regardless of the condition of their leadership is an excellent argument for their not being up in arms about a shutdown. This does not contradict the existence of diffidence by some, but the American people know they can outlast the partisanry of participants in the federal government, and not the other way around. They have already fought and won a war for their independence, and fought again to preserve that union, and succeeded.