Robert Pollin has written a short and very important book titled as this post. Bob is correct in pointing out that the main obstacle to full employment has been political, and that there is no technical reason why we are not pursuing policies that would produce lower levels of unemployment. Note that, as I suggested before, the unemployment problem, as bad as it is right now, is actually worse than you might think.
The full employment goal was attacked almost from the beginning, when it was implemented as the result of the Employment Act of 1946 in the United States. Arguably the Fed-Treasury Accord of 1951 was the first bullet shot in the war against full employment policies. Intellectually, the notion of the natural rate of unemployment, developed by Milton Friedman, and still part of the box of tools of mainstream economists (including New Keynesians) gave theoretical respectability to the idea that full employment could not be a sustainable policy goal.
But it was the rise of conservatism in the 1970s, and the Volcker-Reagan economic policies, that effectively eliminated full employment from the policy agenda. Pollin's book is a plea to bring back the role of the State in promoting policies that would benefit society as a whole. Further, he argues that the same State capacity that has allowed the US to remain a military power can and should be used to promote industrial development with equitable income distribution. A must read!
PS: See also Bob Kuttner's article on Pollin's book at the American Prospect, and Bob's piece in the Boston Review on the topic of his book.