The internals of the new McClatchy-Marist poll display a striking disconnect that goes to the heart of the question of how Obama can win back independents — which is at the core of the political battle over fiscal issues right now. It finds that large majorities of independents agree with Obama on tax hikes for the rich and on Medicare — even as they disapprove of his handling of the deficit and overall performance.

The poll finds that 63 percent of independents support dealing with the deficit by raising taxes on those over $250,000. It also finds that only 23 percent of independents support cuts to Medicare and Medicaid, versus 75 percent who oppose such cuts. Indys are far more in agreement with Obama than with Republicans on the two core questions at the heart of the fiscal debate right now.

Yet the poll also finds that only 28 percent approve of Obama’s handling of the deficit, versus 68 percent who disapprove. And only 42 percent of independents approve of Obama’s performance overall, versus 51 percent who disapprove — a finding mirrored in today’s Post poll.

The disconnect goes to the heart of Obama’s current political challenge. The GOP claim that Obama’s speech was overly partisan is all about damaging him among these voters by portraying him as a divider. Obama advisers have reportedly also concluded that independent voters want him to play a leading role facilitating compromise between the two parties.

At the same time, if this and other polls are any guide, independents are far more in agreement with Obama than with Republicans on taxes and Medicare. That suggests that Obama can also win back independents by forcefully articulating his own positions on these issues — which indys appear to agree with — and contrasting them sharply with those of Republicans.

Obama and his advisers seem to be trying to reconcile these two approaches. By reaching a deal on the Bush tax cuts and signaling a desire to reach compromise at the outset of budget negotiations, Obama is hoping to win back independents who — the theory goes — want a president who rises above partisan squabbling and facilitates compromise among warring factions. At the same time, if Obama’s speech last week is any guide, his advisers also recognize that indys agree with his actual fiscal positions and strongly disagree with the GOP — meaning he should forcefully contrast their visions, even if it means getting tarred as “partisan” by Republicans.

Right now, the numbers look pretty grim among independents. But it’s been less than a week since Obama’s speech, and it will take some time to tell if this balancing act will pay off. This is their playbook. We’ll see if it works.