At a ceremony honoring veterans and senior citizens who sent presents to soldiers overseas, Attorney General Richard Blumenthal of Connecticut rose and spoke of an earlier time in his life. “We have learned something important since the days that I served in Vietnam,” Mr. Blumenthal said to the group gathered in Norwalk in March 2008. “And you exemplify it. Whatever we think about the war, whatever we call it — Afghanistan or Iraq — we owe our military men and women unconditional support.” There was one problem: Mr. Blumenthal, a Democrat now running for the United States Senate, never served...