It looks like POTUS can do it - at least under the 14th Amendment. The arguments against it are political, not legal.
http://www.slate.com/articles/news_a...ic_if_the.html
Here is another article:
http://www.newyorker.com/talk/commen...talk_hertzberg
It was the Republican Party that ensure that the federal debt could not even by questioned, let alone repudiated.
The measure was designed to prevent newly re-admitted Congressmen from the Confederacy from playing mischief with government debt to get revenge - such as refusing to pay Union veteran benefits or paying off Confederate debts.
There is also the issue of who has standing to sue:
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"In the end, Obama could have no honorable choice but to invoke the Fourteenth. There is little doubt that he would prevail. The Supreme Court would be unlikely even to consider the matter, since no one would have standing to bring a successful suit: when the government pays its bills, who is damaged? The House Republicans might draw up articles of impeachment, adopt them, and send them to the Senate, where the probability of a conviction would be zero."
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We live in interesting times.