This seems to have gotten lost in the whirlwind, but remember what the key elements here are.
In exchange for not defaulting on the United States' word of honor, which in any other year would have passed without a word, the Republican extract $2.5trillion in spending cuts.
No revenue increases are permitted to take up any of the deficit reduction in this $2.5trillion figure.
The cuts will be designed strictly by the White House, who become "the ones that cut [Popular Program X]."
Congress heroically rides to the rescue of Popular Program X by voting against the cuts; Obama vetoes, and without Democratic votes to override a Democratic President's veto (which override would devastate the nation's finances anyway), the Republicans are dashed in their valiant attempt to preserve Popular Program X.
This is not a neutral compromise. Neutral would be a debt ceiling increase, and fighting out the budget's spending and revenues when it's time to write the budget. Compromise would be a package of spending cuts and tax revenues. This, if it gets adopted, is a 100% Republican victory.