What if the Democrats decide to unilaterally reopen the government and ignore the debt ceiling? Could the President simply issue an executive order that until Congress passes new legislation, existing law will be used as spending and borrowing authority?
Of course the House would immediately impeach him. I have to believe the Senate would not convict him in a trial - not with the necessary 2/3 majority. And the courts cannot reverse the decision of the Senate; according to Wikipedia "In Nixon v. United States (1993), the Supreme Court determined that the federal judiciary cannot review such proceedings."
An extra benefit of the impeachment trial would be the inevitable overreach of the House prosecuters - with the TP crazies running the show, I can just imagine how stupid and weak their legal case and arguments would look.
Constitutional? Maybe not - but many are saying that we have a "constitutional crisis" now, in several forms - both a debt default and the coup taking place in the House are arguably unconstitutional.
Of course, there would be a SCOTUS review of the executive order - but even that could possibly go in the President's favor if he is only executing existing law and not changing law or policy. And if the economic and constitution crises are severe enough, there might be 5 justices (or their owners) who see the practical necessity of keeping the government running. This might mean the executive order should come after a default so both the cost and the need for resolution are evident.
The House still holds the "power of the purse" - but it would become a more limited power if annual budget levels are considered to be renewed until changed by new legislation. This sounds consistent with the lther checks and balances written into the Constitution - I don't think anyone ever intended this amount of power to be held by a small minority faction.
Setting a precedent that the government cannot and will not be shut down would be a very good thing - if there are changes required, they have to be legislative changes as intended in the Constitution. The ONLY way to change what we do is to win elections and pass laws, or have them declared to be unconstitutional by the court.
I know this is an extreme proposal - but what else are we left with if Boehner is right that a clean CR and debt ceiling increase will not pass the House? (I think they would both pass shortly after a default actually happens, but maybe not.)