The committed obligations of which you speak are the innumerable wasteful, politically motivated “obligations” that have gotten us where we are today. Congress can repeal what it creates. There are sufficient revenues coming into the treasury to cover debt servicing, Soc. Security, Medicare/Medicaid, & defense. The rest is discretionary spending, not legally required to be spent.
In your homey example, you leave out the obvious, most common choice of cutting back. Cable gone. A/C turned up 5-10 degrees or off, if necessary. Nights out - gone. Shopping - no way. Steaks become chicken. Second car sold & insurance canceled. Whatever you can cut.
The very last, most irresponsible thing you could do is borrow money you can't pay back in the expectation of cutting expenses later. And especially so if you have known this was coming for a long time - years. First you cut your expenses to the bone, sell what assets you can, & only after do you consider the extremely dangerous option of getting deeper in debt. No financial adviser would tell you to run down to the credit union for some money to tide you over what could be a permanent cutback in income. Cut expenses now & deeply, not in a couple of months, is what he would say.
Obama, the Rats, & RINOs want to raise the debt ceiling to insure their reelection & maintain power, by directing that money to supporters thru Federal spending. It also saves them from having to produce a budget prior to Obama’s reelection. It has nothing to do with the fear of default.
The debt ceiling is not the edge of the cliff, it is the guardrail in front of the cliff. Raising the ceiling moves the guardrail closer to the cliff, putting everyone but the pols* in greater danger.
*They have a golden parachute.
In the example I gave I said get a small loan to keep the bills paid and maintain the credit rating, then as you recommend, get rid of Cable, buy clothes at a thrift store, cook at home instead of eating out. All things which I already do living on Social Security. Then the costs would come down after several months.