in case a 10-15km mass extinction tier asteroid was heading for earth(with a decade or 2 of warning), would it be feasible in the near future that all the world's governments would cooperate and start massively funding the building spaceports to launch things that could destroy or alter the course of said asteroid?

If yes, I dont think shit like gravity tractors or laser deflection could work.

This leaves 2 options:
1.altering trajectory through nuclear bombs
2.altering trajectory through kinetic energy impacts

for the 1st, how many tsar bomba(~100MT) warheads would be needed to impact on a chicxulub size asteroid to alter its course not to hit earth?

Would humanity be able to shoot dozens of rockets carrying such nuclear warheads in short order, if extinction was the alternative?

Would it be cheaper per launch to use 10-15ton ion engine powered probes that could accelerate to speeds which have enough kinetic energy to alter the course of the asteroid in a few dozen impacts?