From an America-as-superpower perspective this may be true. I would imagine that it feels somewhat different for the the American families who have lost their sons and daughters in the conflicts and for the people of Iraq and Afghanistan.
George W. Bush is fond of describing himself as a "war president." And he has made many decisions involving soldiers and battle. But does this make the description an appropriate one? For many people the answer is obvious. We're engaged in conflicts in Iraq and Afghanistan, after all. But Bill Clinton initiated hostilities in the Balkans twice, George H.W. Bush invaded Panama and Iraq, and neither president ever described himself as a "war president."
For a superpower, being involved in a military conflict somewhere is more the norm than the exception. Since 1945, only one president has not presided over combat that engaged American troops—Jimmy Carter. (Between the Bay of Pigs operation and the American "advisers" in South Vietnam, John F. Kennedy doesn't make the cut.) America remains the world's dominant military-political power, so local crises often engage American allies or interests. Britain was in a somewhat similar position in the late 19th and early 20th centuries. As a result, British forces were fighting someone, somewhere for most of that period. But Britain did not think of itself as "at war," nor would British prime ministers have described themselves as "wartime" leaders. (In fact, Tony Blair has never described himself as such, even though he presided over British military involvement in the Balkans, Sierra Leone, Afghanistan and Iraq.)
America (and before it, Britain) has felt it was "at war" when the conflict threatened the country's basic security—not merely its interests or its allies abroad. This is the common-sense way in which we define a wartime leader, and by that definition the politicians in charge during World Wars I and II—Wilson, Lloyd George, Roosevelt, Churchill—are often described as such. It's not a perfect definition. The United States has been so far removed from most conflicts that even World War I's effects could be described as indirect (incorrectly in my view). But it conjures up the image of a threat to society as a whole, which then requires a national response.
By any of these criteria, we are not at war. At some level, we all know it. Life in America today is surprisingly normal for a country with troops in two battle zones. The country may be engaged in wars, but it is not at war. Consider as evidence the behavior of our "war president." Bush recently explained that for the last few years he has given up golf, because "to play the sport in a time of war" would send the wrong signal. Compare Bush's "sacrifice" to those made by Americans during World War II, when most able-bodied men were drafted, food was rationed and industries were commandeered to produce military equipment. For example, there were no civilian cars manufactured in the United States from 1941 to 1945.
Among the many failings of the Bush Administration, I think the lost opportunity after 9/11 is the greatest. Bush could have put us on a war-like footing. With the nation united behind him, he had one of those once in a generation opportunities to change the course of the country. He could have said then that we are going to move quickly to end our dependence on foreign oil and get ourselves ourselves out of the losing politics of the Middle East. He could have said to the country that it was time for us all to make some real but necessary sacrifices, and the country would have responded. We would be in a much different place today.
Instead he told us to go shopping and he immediately began planning to invade Iraq as well as Afghanistan. And he gave up golf.