Yes, the idea of circumventing the debt ceiling with a $1 trillion platinum coin is weird. But some of the objections to the whole idea are really preposterous. Like this tweet from the National Republican Congressional Committee:
(k) 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 why the platinum coin option could technically work. The Secretary of Treasury can order up a small platinum coin and give it any value he wants. Say, $1 trillion. That coin would be deposited at the Federal Reserve. The Fed would credit the Treasury's accounts with $1 trillion. Now the federal government would have enough money to pay its bills without having to worry about debt-ceiling restraints on borrowing. At least for a little bit.
That sounds outlandish, but it's not all that different from how our system of fiat money already operates. The U.S. government earns a small profit every time it mints, say, a $1 coin and deposits it at the Fed — that's because it costs less than $1 to actually produce the coin. This profit is known as seigniorage, and it's why we don't run into absurd situations like this:
In the modern age, money can be worth more than the material used to make it. The trillion-dollar platinum coin would operate under the same principle — just on a much, much, much larger scale.
--Note that Mike Castle wrote the platinum-coin law with the intention that the U.S. government would earn a small profit from seigniorage. He just never envisioned that it would earn $1 trillion in profit.
--The former head of U.S. Mint agrees: The platinum coin option would work