For purpose of discussion, assume that due to bad luck, this asteroid has evaded the detection of all amateur and professional astronomers until about six months from impact. The asteroid is too large to deflect with humanity's current spacefaring capabilities, and the general scientific consensus is that the impact will end all multicellular life on Earth.
What do those six months look like?
I feel like doctor strangelove probably had it about right. Tbh though, I feel like we ought to have enough nukes to do something. I can perfectly picture us not willing to use our nukes to protect the world though, assuming they even work anymore.
The nukes aren't the problem so much as getting the nukes to the asteroid before it's too late. An ICBM can hit anywhere on Earth but escaping Earth's orbit is another matter, and depending on the angle that the asteroid is approaching from it's possible that we would need to very quickly build the biggest rocket that's ever been built.