I'm pretty sure an X-Prize-style $10 Billion tax free for the next antibiotic from the government[1] would probably get something done. Given our needs, the $10B would be cheap. Heck, buy the next 3 or 4 discovered.
1) assuming said government exempts the company from court claims on the approved drug
The gov't is already looking at something similar. If an antibiotic is approved by the FDA, the company would be guaranteed at least $100M in revenue per year, going up to $350M in the fifth and final year.
1) assuming said government exempts the company from court claims on the approved drug