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That isn’t meant as a rhetorical question. I’d genuinely like to know whether Republicans are grappling with it, and how. That’s because the GOP finds itself trapped in a contradiction that will require that question to be dealt with sooner or later.

Some of the party’s most sacred principles lead to positions that are deeply unpopular. At the same time, many individual GOP lawmakers have clear incentives to continue to hold those positions. They come from safe districts where majorities agree with them, and standing behind them earns praise from conservative interest groups and media. Yet those positions — and their underlying principles — are damaging the party as a whole. Regular association with them may be increasingly damaging the party’s “brand” — Republicans lost the election in part because they were seen as patrons of the wealthy — and they constrain the party from reaching the compromise with Dems the public overwhelmingly wants, hurting its overall image further still.

The new Pew poll drives this home. It confirms again that Dems hold the middle ground in the fiscal cliff battle. But it goes further. Majorities broadly sees the Democratic Party as in line with their priorities on many issues and with their basic sense of how government should solve our problems.

By 53-33, Americans see the GOP as “more extreme in its positions,” while Dems are seen as more willing to work with the other party by 53-37. Fifty five percent say Obama is seriously trying to work with Republicans, while 32 percent say GOPers are trying to work with the President. There’s rising support for the Dem solution to the fiscal mess — a mix of tax hikes and spending cuts — which is now up to 74 percent. Big majorities oppose specific spending cuts — such as cuts to education and infrastructure — and oppose raising the retirement age on entitlements.

Yet individual GOP lawmakers continue to have strong incentives to stick with an increasingly unpopular overall posture: That we should sooner cut deeply into cherished government programs that benefit millions and millions of Americans in order to avoid raising tax rates on the top 2 percent. This predicament is one of the GOP’s own making. As Jonathan Chait puts it: “It was Republicans who elevated the unpopular cause of low income tax rates for the rich to a sacred principle, built an entire party theology around punishing even the slightest dissent from that principle, and then enacted the sacred agenda through a rickety budget mechanism that caused it all to expire after a decade.”

The GOP is in a terrible spot, which is why some conservatives, such as Philip Klein, are calling on Republicans to permanently extend the middle class tax cuts while letting the high end rates go up, to live to fight another day. But it’s unclear whether that solves the basic underlying problem here, which is that the GOP vision of government seems to be fundamentally and increasingly out of step with how majorities view its proper scope and role. The Pew poll finds Dems with significant leads on many other domestic issues, like education, energy, health care, and Social Security. And Republicans are so dedicated to seeing deep (and unpopular) entitlement cuts that they are preparing a showdown over the debt ceiling to achieve them. It’s true that the politics of the debt ceiling don’t automatically favor Dems (because people associate it with over-spending in the abstract). But the GOP brand is so tarnished — even as Obama’s popularity is rising — that the public may implicitly trust the President in the next showdown, too, particularly if he opposes the sort of entitlements cuts the GOP wants.

Yet next year, as now, the incentives for individual GOP lawmakers, particularly in the House, to stage that showdown will remain strong. It’s hard to see how it’s a good thing for the GOP if lawmakers remain comfortably isolated from broader opinion when the party plainly needs to evolve. A non-rhetorical question: Do Republicans view this as a problem?