During the debt ceiling crisis of 2011 and 2013, there was talk about minting a trillion dollar coin to unilaterally raise the debt ceiling via this back-door method if Congress was unwilling to do so. In the end, Obama administration and Congress strucks deals and the debt ceiling was raised both times. In fact raising the debt ceiling had previously been routine and pro-forma and had never been a political issue.
But what if Congress couldn't get it done on time and Obama decided to unilaterally raise the debt ceiling using this trick (rather than defaulting on govt obligations)?
Some background:
The debt ceiling is a cap on government borrowing that was created back in 1917. The debt ceiling has nothing to do with government spending, which is set during the budget process. Raising the debt ceiling simply lets Treasury borrow the money it needs to pay all U.S. bills and other legal obligations. Those bills are for services already performed and entitlement benefits already approved by Congress. The debt ceiling therefore doesn't authorize new spending but authorizes the U.S. to pay what it already spent.
The trillion dollar coin gimmick accomplishes the same thing via accounting trick. Since the treasury now holds this extra trillion dollar "asset", it subtracts from the total debt on paper thus allowing an extra trillion dollars to be borrowed. This gimmick has the exact same monetary affect as raising the debt ceiling by 1 trillion dollars directly. The trillion dollar coin has no greater or lesser affect on things like amount of govt spending, budget deficits, inflation, etc than raising the debt ceiling by that exact same amount.