That's not true. Checks are issued against reserves when direct federal funding isn't available. The reserves are usually in the form of low grade unsecured bonds and aren't useful in international trade or with large investment institutions, but they allow day-to-day business to continue (like paychecks).
It's then the responsibility of the treasury to replace unsecured debts with secured debts prior to maturity.
This is an important point. Yes! Those are obligations that must be paid back to those pension programs. Additionally, lower grade unsecured bonds have been dispersed and need to be accounted for as federal debt.
We both seem to agree on that point that the U.S. Government has ALREADY spent more than the debt ceiling. I happen to be a libertarian, so I agree with your flavoring of the situation: spending MUST be curtailed immediately. But, regardless, in order to maintain our standing as a creditworthy borrower, the debt ceiling must be raised (and it appears as though that vote is imminent).
What has happened in the public arena is that republicans (full disclosure: I voted republican in the last midterm election and the last presidential election; the lesser of two evils (????)) have painted it as though it's an optional increase and that if we could just get our spending under control, we'd be all set. It's just not that simple; the debt ceiling has to be raised to pay current obligations (domestic and foreign). AFTER that's done, then we can talk about fixing the actual problem.
Worse yet, the debt deal spending cuts are designed to slow the increase of the national debt - not cut this year's (or next) actual spending.