Mint the Coin or Be Impeached?

I just had a thought, which is a bit too long for twitter, so I'm putting it here: Doesn't the President HAVE to "Mint the Coin"--i.e. the $1t platinum coin, or whatever combination of coins is necessary--in order to prevent default of the U.S. government, if the Republicans in Congress refuse to raise the debt limit? And, if the President won't do it, is that not grounds for his impeachment? Let me explain. The President is obligated by law to spend X amount of money and to take in only Y amount of revenue (where Y is obviously less than X), and further it is stated in the Constitution that the government is obligated to honor its debt. If the Congress does not raise the debt ceiling, then these laws would seem to come into conflict. However, as we all now know, there is also a law in force with plain language allowing unrestricted platinum coinage in any denomination. Thus, the President could direct the Secretary of the Treasury to do this, and thereby keep from violating one of the laws. Would it not therefore be an impeachable offense for the President to violate the Constitution by refusing to mint the platinum coin? Is he not required to do this, since it is permissible and would allow an obvious way to mutually uphold the budget and revenue provisions legally in force? So, to my mind, the issue is not *COULD* the President (through the Secy Treas) do this and survive Supreme Court scrutiny, or *SHOULD* the President do this as a matter of policy or politics, but rather that he *MUST* do this, unless they can find another way around the debt ceiling. As I see it, it is the President's obligation to uphold the Constitution, in conjunction with the revenue and spending laws duly enacted by Congress and signed by the President. If the President refused to Mint the Coin, would he not be subject to impeachment for refusing to implement the laws of the land using a clearly available means? Hence my conclusion, Mr. President: Mint the Coin, or Be Impeached!