The BPC wants Congress to follow an "accelerated regular order" -- meaning, no Senate filibusters allowed and committees of jurisdiction do all the work -- to pass a deficit reduction package. That sounds reasonable, but Senators would have to agree to carve out an exception to their right to filibuster in this case. In fact, the same result could be achieved by following the reconciliation process, as was done to pass Obamacare.
The real flaw in the proposal is the demand for an automatic "backstop" that would occur if Congress failed to adopt the required laws. The last time we tried that, barely a year ago, it was called a "sequester" and now everybody is complaining that they passed it. The BPC explain this backstop this way:
The Executive Branch shall eliminate any shortfall – whether from the failure of the debt reduction bill to become law or from insufficient debt reduction contained therein – by achieving the requisite amount of debt reduction compared to the current policy baseline: half of the savings would come from reductions to all mandatory and entitlement programs (with the exception of Social Security) and half from reductions in all federal tax expenditures. The framework recognizes that the backstop of cuts in mandatory programs and tax expenditures will require flexible treatment – certainly, cutting an entitlement program involves different considerations than cutting a tax expenditure.
I really don't see how the President alone, absent votes by Congress on new laws, could reduce spending on mandatory and entitlement programs, and especially not on tax expenditures. Remember, his chief constitutional responsibility is to see that the laws are faithfully executed. If the law says people get a tax deduction for a charitable contribution or home mortgage interest, how can the President can change the law or the tax collection rules or the forms to make that happen. Dumb idea in pursuit of a worthy goal.