One suggested way to address the debt limit challenge is for the U.S. Treasury to issue a trillion-dollar coin and then deposit it with the Federal Reserve System as cash. I'm not a lawyer, so I will not opine on the legality of any proposed action. However, I can read. I can look up the law. I can post it herewith.
The authority for minting a trillion-dollar "platinum" coin appears to come from U.S. Code 31, #5112, subsection (v). The reference is to palladium, which is in the family of "white gold" platinum elements, but has different characteristics from platinum. Note that the law in clause (v) (3) sets a minimum price for any minted coin, i.e., the cost of acquiring the metal and the cost of minting the coin. It does not have a maximum price. Here is the entire subsection, from the Cornell Law School website (see link at the end).
(1) Subject to the submission to the Secretary and the Congress of a marketing study described in paragraph (8), beginning not more than 1 year after the submission of the study to the Secretary and the Congress, the Secretary shall mint and issue the palladium coins described in paragraph (12) of subsection (a) in such quantities as the Secretary may determine to be appropriate to meet demand.
(A) The Secretary shall acquire bullion for the palladium coins issued under this subsection by purchase of palladium mined from natural deposits in the United States, or in a territory or possession of the United States, within 1 year after the month in which the ore from which it is derived was mined. If no such palladium is available or if it is not economically feasible to obtain such palladium, the Secretary may obtain palladium for the palladium coins described in paragraph (12) of subsection (a) from other available sources.
(B) The Secretary shall pay not more than the average world price for the palladium under subparagraph (A).
(3) Each coin issued under this subsection shall be sold for an amount the Secretary determines to be appropriate, but not less than the sum of—
(B) the cost of designing and issuing the coins, including labor, materials, dies, use of machinery, overhead expenses, marketing, distribution, and shipping.
(4) For purposes of section 5134 and 5136, all coins minted under this subsection shall be considered to be numismatic items.
(5) The Secretary may issue the coins described in paragraph (1) in both proof and uncirculated versions, except that, should the Secretary determine that it is appropriate to issue proof or uncirculated versions of such coin, the Secretary shall, to the greatest extent possible, ensure that the surface treatment of each year’s proof or uncirculated version differs in some material way from that of the preceding year.
(6) Coins minted and issued under this subsection shall bear designs on the obverse and reverse that are close likenesses of the work of famed American coin designer and medallic artist Adolph Alexander Weinman—
(A) the obverse shall bear a high-relief likeness of the “Winged Liberty” design used on the obverse of the so-called “Mercury dime”;
(B) the reverse shall bear a high-relief version of the reverse design of the 1907 American Institute of Architects medal; and
(C) the coin shall bear such other inscriptions, including “Liberty”, “In God We Trust”, “United States of America”, the denomination and weight of the coin and the fineness of the metal, as the Secretary determines to be appropriate and in keeping with the original design.
(7) Any United States mint, other than the United States Mint at West Point, New York, may be used to strike coins minted under this subsection other than any proof version of any such coin. If the Secretary determines that it is appropriate to issue any proof version of such coin, coins of such version shall be struck only at the United States Mint at West Point, New York.
(8) The market study described in paragraph (1) means an analysis of the market for palladium bullion investments conducted by a reputable, independent third party that demonstrates that there would be adequate demand for palladium bullion coins produced by the United States Mint to ensure that such coins could be minted and issued at no net cost to taxpayers. http://www.law.cornell.edu/uscode/text/31/5112