The biggest problem with not raising our national debt is that when we run out of borrowing authority, we end up with a huge, confusing mess. What bills get paid first, which ones do we slow pay, and what promised spending do we slow down or cancel?
The lack of clarity is entirely unnecessary.
The natural place to put the authority to trim our fiscal expenditures in line with income is with the president. The President is in charge of faithfully executing the laws. The executive is the first to know when money arrives and is available to be spent. Though it will be politically uncomfortable for a Republican majority House to give a Democrat President this authority, it would make clear that avoiding Greek style fiscal collapse is more important for the GOP than temporary political advantage. In such a scenario, not raising the debt limit would allow Democrat priorities to be protected while Republican spending priorities would go under the knife.
None of the corporatists that heavily fund both parties would like legislation that laid out who had the power to make the cuts but it would be difficult to resist a bill that makes it perfectly clear that it is the job of the government to make cuts hurt the least and not the opposite in order to bring political pressure to bear to restart the irresponsible flow of red ink.