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And, short of just printing new money, reaching the debt limit most definitely limits how much Congress can spend. That's why govt shut downs occur or are threatened.
You also neglect the fact that debt rollover isn't instantaneous. There is a period of time, no matter how brief, that the debt limit is exceeded in the process if you're already at the limit from meeting other obligations.
It is absolutely "instantaneous". Government accounting 'books', or any other entity for that matter, are only 'closed' at the end of the day. I.e., I can sell a new Treas bond at 9 AM and pay you off at 4 PM and still not legally exceed the debt limit. I posted proof of this before back during the previous 'cliff' crap when the likes of you and yllus were making this ridiculous argument. This is how Geithner was able to 'juggle the books' for several months pending the deal (sequestration).
I.e., the "brief period" theory is utter rubbish.
Do you think when you refinance your home mortgage the law is broken if you sign the new loan before they legally dismiss your old one? Under your theory the loan contract would be breached - you can't have two first mortgages outstanding simultaneously without committing fraud, right?
And how do you get released from your original home loan without first paying it off? Isn't how you pay it off with the proceeds of the new loan? So, the new loan exists before the original is paid off. It all comes down to 'the end of the business day'.
Your "brief period" theory is bunk.
Fern