This. The political reality is that people scream bloody murder when even the "small ticket items" are changed. There is no possible way the people and the politicians they elect will face and solve this budget crisis in time to avert a crisis. The NYT "game" should have had one check box at the bottom labeled "continue to borrow until the dollar is destroyed". But people dismiss this danger as just abstract theory and rationalize it on the Russian Roulette Principle (we got away with it in the past).
As an aside, there are all sorts of unidentified or implicit errors and bad theories built into this game which makes it a pointless exercise and impossible to actually judge. For example, If you reduce the tax break for employer-provided health insurance it shows up as a spending cut but that is actually a tax increase on imputed income. Another example is that if you cap Medicare growth the economic implication (especially if inflation takes off) is price-fixing or rationing of services. This is Econ 101 (it won't work) but the average person probably does not have the analytic skills to see the cap for what it is.