If you want to stop running up charges on your credit card, you cut up the card, not your bill. You've already made the charges, and you need to pay the bill.
By refusing to raise the debt limit by refusing to pay expenses that Congress has already charged members of Congress like Rep. Jason Chaffetz and Sen. Mike Lee are foolishly damaging America's credit rating by recklessly refusing to pay its bills. In the end, that will only cost us more as our interest rates will rise.
When Congress votes to spend money it doesn't have (and sometimes it should do that, like in economic downturns), the decision to take on more credit should be made when the money is appropriated, not when the bills come due.
If Chaffetz, et. al., want to stop deficit spending, they need to get Congress to stop spending, not stop paying its existing obligations.