The GOP doesn't need the President to agree on a budget-balancing plan; they control the House, and all spending bills must originate in the House.
If the GOP wants a balanced budget, they need to pass a balanced budget - "You've got $2.2 trillion in revenue coming in; here's authorization to spend $2.2 trillion ... take it or leave it".
Presto! Balanced budget! No need to raise the debt limit!
Of course it will be painful - it will lead to years of economic agony.
But there's three choices - amputate the gangrenous toe now, amputate the gangrenous leg a little later on, or die. Which one do you want?
Pick one. "None of the above" is not an option.
Please explain why its economic agony? Because there won’t be this extra trillion in the economy? Or because these bozo’s in Congress will have to explain to their “handout” constituency that we’ve had to cut their favorite cell phone giveaway program or close their favorite military base?