One of the ways in which Catch-22 is an American novel is the balance between blind patriotism and common sense. The characters are all bound by their patriotic duty to their country; they want to serve and be seen as serving, but are scared of their own well-being as well. This is a common reaction to war and to military duty; since the draft was still in effect when the book was written, the soldiers fighting had no choice but to serve. Their service is seen as something required, without an alternative, but also as something that should be instinctively chosen by dint of patriotic duty.
In the most widely-quoted paragraph, the infamous Catch-22 is discussed:
Orr was crazy and could be grounded. All he had to do was ask; and as soon as he did, he would no longer be crazy and would have to fly more missions. Orr would be crazy to fly more missions and sane if he didn't, but if he were sane he had to fly them. If he flew them he was crazy and didn't have to; but if he didn't want to he was sane and had to.
(Heller, Catch-22, Google Books)
This is the "catch" that caused so much opposition to the draft system; a sane man would never volunteer for military duty, so he is perfectly suited. For a patriotic man, service would be voluntary, but the draft system caused everyone to suffer, not just those who chose service. The higher ideal of "American patriotism" pushed int the 1940s became a draw towards individual sacrifice by the government going into the 1960s, causing the book to become a must-read for the burgeoning counter-culture.