the issue of the Debt Ceiling was settled in 1868 with the passage of the 14th Amendment ... specifically SECTION 4.
"The validity of the public debt of the United States, authorized by law, including debts incurred for payment of pensions and bounties for services in suppressing insurrection or rebellion, shall not be questioned."
NOTE: "public debt of the United States, authorized by law" When Congress passes the legislation and the President signs it, the debt becomes valid and there is no limitation imposed by an imaginary "Debt Ceiling". However, since it is enacted as law, and contradictory to other laws – the legislature is violating the law by authorizing obligations which exceed the debt ceiling – that is, the member of Congress who proposed the debt is violating the law and is a criminal. We can extend that to all members, including the President, as accomplices after the fact – but the burden of criminal behavior goes to the one introducing the legislation. It is the obligation of CONGRESS to ensure it conforms to its own laws, and the President to veto if he has cause to believe those laws were violated … a expectation of the debt ceiling being raised shields the President, but not those in Congress who fail to vote on, or oppose, a proforma raising. When the Republican Party supported the cutting of tax revenue that was a part of the new, and enacted, health Care Law, they were engaged in a willful violation of the Constitution and Law … one which justifies their removal from Congress.
In theory, all employment associated Legislative Acts creating National parks are a matter of LAW and therefore can be kept open with payments made. the same would go for the creation of any agency as a mater of legislative action. The very idea of a shutdown is -- in a Constitutional context -- illegal, unless legislation is enacted to create it.