Want a sense of the scope of the GOP's internal divide between conservatives and the party establishment? Take a look at some recent poll numbers that paint a fuller picture of just how many of the Republican Party's core elements object to the direction of the party.

A CBS News poll released Tuesday evening found what most other polls have recently: the Republican Party suffers from a negative impression among most Americans.

Sixty percent of all U.S. adults, the CBS poll found, have an unfavorable opinion of the Republican Party, versus 31 percent who have a favorable opinion of the GOP.

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Democrats, expectedly, have strongly negative opinions toward Republicans; self-described independents are also sour on the GOP, 60 to 24 percent.

A closer look inside the numbers, though, tells the deeper story.

One in four self-described Republicans, 25 percent, also said in the CBS poll that they had a negative opinion of their own party – an ominous sign as the GOP searches for a pathway back to electoral success.

Much of the news about efforts to remake the party, such as the Republican National Committee's new "Growth and Opportunity Project," have been confined to an inside-the-Beltway audience. Much of the outreach called for by the report has yet to take place, making any improvement in voters' impression of the party a lagging indicator.

Moreover, the GOP's internal angst might not necessarily be surprising given the party is still reeling from its loss in a second consecutive presidential election. More recently, party leaders cut a deal that allowed taxes to rise -- a prospect that's anathema to the Republican base.

The CBS poll doesn't offer more detailed breakdowns, but looking inside the internal numbers of the NBC News-Wall Street Journal poll late last month and a CNN/ORC poll released in mid-March offer clues to the source of internal Republican discord.

Both polls found that blanket "Republicans" had a slightly more favorable opinion of the Republican Party than in the CBS poll. The NBC/WSJ poll, conducted in late February, found that 63 percent of Republicans had a favorable opinion of the Republican Party, versus 15 percent who expressed a negative impression; 21 percent of self-described GOPers were neutral. Similarly, 82 percent of Republicans rated the party favorably in the CNN poll, versus 14 percent who had an unfavorable opinion of the GOP.

It's among conservatives where opinion turns against the Republican Party establishment.

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Less than half of self-identified conservatives -- 48 percent -- expressed a favorable opinion of the Republican Party in the February NBC/WSJ poll. Twenty-six percent of conservatives had a negative opinion of the party of which they ostensibly serve as the base, and a quarter -- 25 percent -- were neutral.

The CNN poll includes similar numbers; that poll, which was conducted from March 15-17, found that 58 percent of self-identified conservatives have a favorable opinion of the Republican Party, versus 36 percent who hold an unfavorable impression.

The numbers cut to the core of the GOP's identity crisis. Party leaders wish to broaden the party's appeal and, on some issues (like immigration reform), move toward the political center. That extends to primary elections, in which the GOP establishment hopes to re-assert itself, and avoid instances where unelectable conservatives sometimes topple candidates regarded as more electable in the general election.

To be sure, too, these numbers don't necessarily suggest that conservatives are so disaffected that they would stay home in general election contests. Even the most critical of conservatives eventually came around last fall to supporting Republican presidential nominee Mitt Romney.

But these numbers suggest that the party's right flank -- the heart and soul of the Republican Party -- haven't bought in. And until they do, a transformation of the party will be that much more difficult.