While it is certainly the case that far more Americans self-identify as conservative than as liberal, it's not clear that it matters very much. Klein links to a paper by Christopher Ellis and James Stimson that dates the dominant lead in "conservative" self-identification to the mid-1960s. That would be important if it corresponded with a transition from conservative to liberal electoral victories, but it doesn't, really. Congresses in the 1970s and late 1980s were far more liberal than those of the 1950s, even though conservatives had opened up a wide lead in self-identification -- a lead that didn't disappear when liberal candidates won in 2006 and 2008. Klein concludes:
The word "liberal" is not popular, it has never been popular, and I do not expect that it ever will be popular. But liberalism -- and the politicians who support it -- are doing just fine. Not in any given election, of course, but over time. It's not obvious that a stronger brand has done much for the right, nor that it has seriously hampered the left. Branding might be important. But product matters more.Sounds about right to me.
By the way, if you're interested in changes in public opinion over time, I'll pass along a couple of other things to look at. Michael Robinson looked at Pew data and found ideological self-identification flat over 1987 through 2008 (summary; full paper). And getting away from the words "liberal" and "conservative" to views on specific issues over the earlier period that Ellis and Stimson cover, I recommend William G. Mayer's The Changing American Mind, which looks at survey data on a wide variety of issues over the period 1960-1988.