I already touched on today’s new Post poll this morning, but there are a bunch of numbers in here that really deserve their own post.

To wit: It finds that only 23 percent of Americans — that would be fewer than one in four — believe the Republican Party is “in touch with the concerns of most people in the United States today,” while 70 percent believe that it is “out of touch.” Among independents, those numbers are 23-70. Among moderates they’re 20-75.

By contrast, Americans say by 51-46 that Obama is in touch. Among moderates that’s 56-42 (he fares worse among independents, 44-53, though far better than Republicans).

At the same time, the poll finds the public siding with Obama and Democrats on many major issues surveyed. Americans disapprove of the sequester cuts, 57-35 — cuts that Republicans are describing as a “victory” for them. Americans support a path to legality for illegal immigrants by 64-32. In fairness, the poll doesn’t test citizenship specifically, so this finding is somewhat inconclusive, but a new CNN poll finds that 84 percent back a path to citizenship for undocumented immigrants who have a job and pay back taxes.

Meanwhile, on guns, the new Post poll finds that Americans support a law requiring background checks on gun sales at gun shows or online by 86-13. A majority, 55 percent, believes it’s possible to make new gun control laws without interfering with gun rights.

On guns, there’s an interesting nuance here. While big majorities favor expanded background checks, it’s not a motivator of voting: Americans say by 60-29 that they could vote for a candidate who disagreed with them on gun control. That helps explain why Republicans don’t really fear any public backlash on this issue.

But my question is: At what point does failure to support proposals designed to address the problems facing the country — ones backed by majorities — create a serious enough general problem for the GOP, by contributing to an overall sense that the party has simply ceased being capable of compromising on solutions to the major challenges we face? The GOP’s awful “in touch, out of touch” numbers would seem to get at this.

This is meant as a real question. We keep hearing that issues such as guns don’t rank high in importance for voters. We keep hearing that the party’s image doesn’t matter too much, because Republicans will all but certainly be able to hold the House. We keep hearing Republicans have a strong incentive not to cooperate with Dems, since many of them are in safe districts. All of that makes some sense.

But is there any point at which the party’s overall image — and its unpopular stances on specific issues — actually do begin to matter in some concrete way? Is there any point at which it becomes clear that the current GOP strategy — make a deal with Democrats on immigration, but nothing else — is insufficient? What would that look like? Anyone?

Greg Sargent writes The Plum Line blog, a reported opinion blog with a liberal slant -- what you might call “opinionated reporting” from the left.