Right now, the primary fear among senior Obama administration officials is that John Boehner and the GOP leadership don’t grasp just how damaging Obama believes it would be to the remainder of his tenure — and the office of the presidency itself and the proper balance of power between it and Congress — if he were to concede anything in exchange for GOP support for a debt limit hike.

Yesterday’s meeting between Congressional leaders and Obama, in which he reiterated his refusal to negotiate over the debt limit, went some way towards driving that home to the Speaker, senior administration officials believe. But there’s still some worry that perhaps GOP leaders still think the President will fold in the end, and that as a result, they still don’t grasp just how much pressure there is on them to resolve internal party differences that are making it impossible for Boehner to agree to raise the debt limit without extracting concessions Tea Partyers would view as a victory.

Obama and his senior advisers view the debt limit battle as a “must win” fight — not one where the difference can be split in any meaningful sense. They see it as a battle that, if not concluded decisively, could have lasting ramifications not just for this presidency, but for others to follow. Some of this has to do with the electoral calendar. If Obama were to offer up anything meaningful in the way of policy concessions in exchange for a debt limit hike now, that would only make a worse showdown more likely later, particularly in 2014, when members of Congress are up for reelection and Republican lawmakers are facing possible primary challenges, particularly in conservative districts.

Publicly, the President escalated his warnings today about what default would mean for the country, and the Treasury Department released a report warning of the consequences brinksmanship itself would have for the economy.

Beyond this presidency, Obama and senior officials think that if the debt limit continues to be seen as a legitimate lever with which to extract major policy concessions, it could mar the appropriate balance of power between future presidents and Congresses. This is a defining moment, one in which it is imperative to stabilize the imbalances that continue to convulse our system, largely due to the deeply unhinged expectations of the Tea Party, and the outsized influence it continues to wield over the GOP and its leadership.

Obama liked to say in 2012 that the election would break the Tea Party fever — or “pop the blister,” as he put it. That obviously didn’t happen. Now — given the calamitous damage default could unleash, and given the continued damage future threats of default could do to the economy and political and governmental system — a clean and decisive victory is viewed as an imperative.

By this same metric, of course, a cave — should it happen, which Obama is adamantly resolved against — would be a catastrophic, epic failure.

There are reasons Republicans might be tempted to look back at Obama’s previous willingness to legitimize — by agreeing under political duress to a terrible austerity deal in 2011 — the idea that the debt limit is a legitimate lever for extracting policy concessions. But such conclusions fail to reckon with the profound differences between the two different moments. Still, liberals and some Congressional Democrats, too, look to 2011 and worry about a rerun.

The principle articulated internally is simple. Never mind delaying or defunding Obamacare — there will be no policy concessions in exchange for a debt limit that would damage Dem priorities. Republicans must refocus on legitimate legislative means, i.e., the legislative process’ normal give and take. In exchange for the debt limit hike, there will be no medical device tax repeal. No Keystone pipeline. Obama administration officials are open to the possibility of face saving moves by Republicans being part of the endgame, but only ones involving process — not policy concessions — such as the McConnell provision, a device floated last year that would have largely transferred debt limit authority to the president.

Senior Obama officials recognize that the political fallout from the debt limit fight could easily blow back on the President to some degree, but on balance believe it puts the GOP in significantly more danger.

Senior administration officials believe that as default looms, Republican leaders very well may realize that this problem is on them to solve. But they are by no means certain this realization will dawn in time, and even if it does, nor are they certain whether Republican leaders can solve their internal divisions or that John Boehner will summon the will necessary to alienate the hardliners in his caucus if those divisions can’t be resolved. And so the possibility of serious miscalculations — leading to disaster — remains very real.