Kevin Drum presents evidence from The Pew Research Center (PDF) showing the public identifying much more strongly with the Democratic Party (50%-35%), supporting increased spending on government programs, and becoming less supportive of social conservatism.
Why did this happen? The best way to understand these shifts is with the concepts of "macropartisanship" and "public mood" developed by UNC political scientist James Stimson. Stimson's work shows that public mood -- an aggregate measure of support for more or less government -- tends to move in the opposite direction from policy (after some lag), acting like a thermostat of sorts against overreach in one direction. Stimson's chart of public mood from 1952-2004 illustrates the pattern nicely:
Similarly, macropartisanship -- an aggregate measure of party identification -- varies systematically in response to party performance. As such, it is not surprising that the public has slowly turned against Republicans given President Bush's persistent unpopularity.
(For more, see Stimson's books Public Opinion in America and Tides of Consent and his co-authored book The Macro Polity.)