Can Obama refuse to negotiate over the debt ceiling?

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6. there are a few possible options as i see it:

1) come to SOME agreement that raises the debt limit.
2) convince to media that republicans are the jerks here and force them to cave.
3) invoke the 14th amendment -- untested, and i think it's a temporary remedy at best. republicans can always force the issue when the annual appropriations bill come up.
4) mint a trillion-dollar coin. untested, but i'm not sure it wouldn't work. the right-wing will howl the government is "printing money" ("minting money" would be more accurate and also alliterative, but it hasn't been imbued with the negative connotations that "printing money" has) but it's kinda funny money anyway and as obama says, congress authorized this spending in the first place.
5) selectively default on certain government obligations. i think the social security trust fund offers that possibility because they get issued a special series of treasuries, so a default on those wouldn't affect anyone else, and treasury would make social security whole once the situation is resolved. but, ... ugh!