Update From the Wilderness
Marc Ambinder checks in from the RNC with a perceptive breakdown of Republican strategery during the party's first month fully out of power:

Here is the basic diagnosis of what ails the Republican Party from Dr. Mitch McConnell, the Senate minority leader. The internal organs are fine. No problem with the composition of the blood that pumps through the party's activist veins. The brain is top-notch -- Republican ideas are well considered, broadly desired, and politically feasible. The body, however, looks ragged; the accent is too...regional (Southern?). [...] The "sales job" theory is quite attractive to many Republicans because it relieves them of having to question whether Americans, at their corps [sic], are beginning to distrust what the party stands for, what the party does, who the party is. What a relief! All that's need are some cosmetics. Maybe it's Mabeline. McConnell's view is shared by many Republican current office-holders. It is not the view that Republican strategists tend to hold, and it certainly is not the view of the younger conservative intellectuals, like the Atlantic's own Ross Douthat and Reihan Salam. The massive data compiled by Gallup about party identification suggests that the party has an identity problem.

Other evidence, including exit polls from 2006 and 2008, locate this problem at a microskeletal level: it cannot deal with globalization, with a flat world, with religious diversity, with institutional decay. Since the 1960s, the GOP's DNA has dutifully replicated activist cells to inflame and attack on culture, and Democratic efforts to minimize the demands and pressure of culture haven't worked. The selection of Sarah Palin got them replicatin' again, but then reality -- in the form of a global economic crisis -- intruded, and Republicans couldn't fight their way out of a plastic bag.

I guess that Mitch McConnell, as the current embodiment of institutional Republicanism, pretty much has to say what he's saying here: admission that the product is flawed, not just the packaging, amounts to pointing a big finger at himself. This is not something that career politicians of any stripe tend to do.

But ultimately I think American parties recede into long-term minority status when their internal contradictions become too glaring for the median weak or non-partisan voter--the guy or gal who voted for Reagan, then Clinton, then Bush, then Obama--to ignore. It happened to the Democrats from the late '60s through the early '90s, when they were perceived as too willing to futz with the operations of the market in pursuit of specific outcomes but not willing enough to assert American prerogatives abroad or concede the relevance of certain moral/behavioral standards ("crime is bad").

They started to come back when, one, Bill Clinton took steps to close the gap between those two views--a more laissez-faire, business-friendly approach to economic policy, a more assertive position in foreign policy--and less crucially two, when the country began to evolve toward the liberal worldview on social issues like gay rights. Once this was resolved, the Judis/Teixeira hypothesis of a Democratic majority forged by structural and demographic factors made sense; the emergence of that majority was delayed, but not derailed, by the 2000 election shenanigans and the national derangement of 9/11 as well as the Republicans' tactical and organizational superiority in the two Bush elections.

Once the Democrats had the better candidate and organization, as well as the wind of Bush's failures at their backs, they emerged as the clear majority party last November. That this trend isn't even necessarily complete is shown by some fairly stunning Gallup data released yesterday: as of 2008, Republicans dominated (in terms of a double-digit advantage in partisan identification) in just four states--Utah, Wyoming, Idaho and Nebraska. The Democrats enjoyed a double-digit edge in 29, plus four more with a nine-point advantage. This hasn't necessarily played out in national elections--McCain won Arkansas, Kentucky and Missouri despite a strong generic Democratic advantage, owing presumably to the difference between a Kentucky Democrat and, say, a Rhode Island one--but it shows just how big a structural problem the Republicans have.

Thus, now it's the Republicans' turn to resolve their big glaring contradiction: a seemingly bottomless appetite for use of force abroad and moral compulsion at home, coupled with an absolute hands-off view toward the economy and contempt for redistributive social welfare in almost all its forms (the home mortgage deduction still seems aces with them). This mix of views helped get the country into the current mess, and offers seemingly no value in extracting us from the troubles.

The internal ferment that crested with Bill Clinton's plurality presidential wins and Barack Obama's majority win began in the 1980s with groups like the Democratic Leadership Council and the emergence of "New Democrats" like Gary Hart, Bill Bradley and Clinton himself. One can perceive the first signs of something similar amongst the Republicans, notably including the efforts of Douthat and Salam that Ambinder references; their prescription seems to involve at least a more serious engagement with economic concerns, first articulated in the "Party of Sam's Club" article I linked to years back and more comprehensively in their book Grand New Party, which I still haven't read. But those ideas haven't yet penetrated official Republican policy deliberations, such as they are.

Meanwhile, some on the right are considering it a symbolic victory that Obama's stimulus plan failed to win a single House Republican vote. But my guess is that the political optics just confirm how out of touch they remain.