It's not going to cost the government anything, when they destroy the government. That is exactly their intent.
"I don't want to abolish government. I simply want to reduce it to the size where I can drag it into the bathroom and drown it in the bathtub." - Grover Norquist, an unelected person, who many Republicans in congress signed a pledge to.
We're at the "small enough" phase, and soon enough we'll be at the "drowning" phase. This is their dream come true, unfortunately it's going to be a nightmare for everyone but the most wealthy.
This is literally going to cost the government more money.