I'm personally hoping Obama goes for the Platinum Coin option. Here's how it works:
1. Section K of 31 USC § 5112, the "Denominations, specifications, and design of coins" section of federal law reads as follows:
The Secretary may mint and issue platinum bullion coins and proof platinum coins in accordance with such specifications, designs, varieties, quantities, denominations, and inscriptions as the Secretary, in the Secretary’s discretion, may prescribe from time to time.
That's it. That's the entire US law regarding what kind of platinum coins the Secretary of the Treasury can issue.
2. The President can make the Secretary of the Treasury mint coins by executive order.
3. If Obama wants, he can sign an executive order ordering the Secretary of the Treasury to issue four platinum coins worth one trillion dollars each.
4. Presto! The budget is now balanced due to a sudden influx of 4 trillion dollars into the Federal Reserve which can then be used to pay off outstanding treasury bonds and get rid of the debt that those represent, pushing congress miles away from the debt ceiling.
5. Everyone briefly flips their shit, but eventually calms down, just like when we went off the gold standard. Demand for treasury bonds goes up hugely, because the Treasury just did something big to say that they are super serious about being willing to pay back those bonds no matter how stupid Congress gets about the budget.