I still say that if President Obama does not pay existing debts as they become due, then he would in fact be violating the law - and hundreds of them at least. Indeed, the situation would surely constitute a "conflict of laws and authority" under innumerable statutes and Articles of the Constitution. Yet, in conflict of law situations, specific statutes take precedence over general ones (including resolutions such as the Debt Ceiling Resolution)
Remember, all these expenditures are called for, and are in fact required, under existing law. Also, non-passage of the Debt Ceiling Rule or Resolution (it is not a statute) does not change that. Furthermore, it is a specific duty of the President to see that the existing laws are executed and carried out. In fact, not to do so might make him guilty of constructive impoundment, insofar as the "President does not have the inherent power to refuse to spend" sums authorized by existing statutes. (Train v. City of New York, 420 U.S. 35 (1975).)
Based upon the above, I would suspect that should the President fail to expend sums called for by and under existing statutes (like Social Security payments), there will be a cascade of law suits filed against him to do so.
I would also respectfully contend that if Congress wishes to prevent these payments under existing statutes, they would have to change every single statute which authorizes, and even mandates, the President to make said already Congressionally authorized payments and monetary obligations.
Additionally, because of the above, I would assert that the Debt Ceiling Resolution is an improper usurpation of Article II (Presidential) power and authority, because it prevents the President from carry out and enforcing existing law, and by a resolution no less. Again, all these spending statutes will still be on the books come August 2nd.
On the other hand, the Debt Ceiling Resolution could also be found unconstitutional because it improperly delegates power and authority to the President to decide which bills are to be paid and which bills are not to be paid. In short, the President does not have the Constitutional power to decide which specific bills are to be paid or not paid (Train v. City of New York, supra).
Besides that, the Debt Ceiling Resolution is also vague, overbroad, and arbitrary, and probably unconstitutional for that reason as well. For sure, it will create an unresolved conflict between hundreds (if not thousands) of statutes and that singular Debt Resolution.
Then, of course, we have the President's inherent power to deal with a national crisis or national emergency. In the Youngstown Sheet and Tube Co. v. Sawyer Case, the Supreme Court concluded that the President had inherent power to seize the American steel companies during a threatened strike. Of course, failure to give full faith and credit to valid debts is much more serious than a threatened steel industry strike. Moreover, when you combine this inherent emergency power with Section 4 of the 14th Amendment of the U.S. Constitution, the President has a very, very powerful hand in this matter. Remember, "the Constitution is the supreme law of the land."
Bill Clinton recently gave very good advice on this subject, and I just hope President Obama will listen to it. Clinton thought that requiring a revote -which is what the Debt Ceiling Resolution requires - on an existing valid law was patently ridiculous.
Finally, because Social Security is currently backed by Treasury Department obligations, if the Federal Government pays any other Treasury Department obligations, foreign or domestic, then it should be required to place all Social Security paper on an equal footing. This is also where Section 4 of the 14th Amendment of the U.S. Constitution becomes extremely important again.