As evidence, Chris Bowers of Open Left cites the "New Democrat" and "Blue Dog" House coalitions as evidence of the Democrats being "more moderate" than the GOP.
What he neglects to mention is that this is all a show of framing. Of course Democrats want to be seen as "moderate." It not electorally beneficial to be seen as a liberal any more. When's the last time you heard a Democratic candidate for office proudly proclaim "I'm an old-style liberal"? The Democrats have had to choose between calling themselves "moderate" and calling themselves "progressive."
And it's because the American people themselves are not liberals. They're heavily weighted to be centrists and conservatives. "Conservative Democrat" is an oxymoron, but you still see Democrats trying to claim the mantle.
As a Republican, however, it pays to try to be a clear and consistent conservative, no matter if you actually are one. You don't see Republicans forming "moderate Republican" coalitions because there's a negative stigma attached.
Democrats are just as liberal as they always have been and Republicans are just as moderate. The framing and terminology has changed. In most parts of the country, it's an electoral mistake to run as a "liberal Democrat" and it's an electoral mistake to run as a "moderate Republican." But there is no "death of the moderate" to be found here.