The one thing Obama absolutely cannot do under any circumstances is negotiate over the statutory debt limit.
The reason is that Republicans are essentially asking for an end to constitutional government in the United States and its replacement by a wholly novel system.
From Jonathan Strong’s report at NRO, what Republicans want in exchange for agreeing to not default on the national debt is a one year delay of Obamacare, Paul Ryan’s tax reform, the Keystone XL pipeline, partial repeal of the Clean Air Act, partial repeal of bank regulation legislation, Medicare cuts, cuts in several anti-poverty programs, making it harder to launch medical malpractice lawsuits, more drilling on federal land, blocking net neutrality, and a suite of changes designed to make it harder for regulatory agencies to crack the whip.
Things like this do happen. The British system of government used to feature a ruling monarch who was checked in limited ways by two houses of parliament. Over time, those houses of parliament leveraged their control over tax hikes into overall control of the government. On a somewhat slower time frame, the elected House of Commons nudged the House of Lords out of almost all of its de facto political power. And that’s the House’s proposal here. The president should become an elected figurehead (not dissimilar to the elected presidents of Germany, Israel, or Italy) whose role is simply to assent to the policy preferences of the legislative majority.
They aren’t even pretending to care about democratic representative government. They’re just out to use whatever brute force they have to get what they (or their masters) want.