It's really really unrealistic from the beginning.
A asteroid the size of Texas is headed towards earth, instead of nuking it directly from earth they decided to drill it.
Instead of sending astronauts, they send oil drillers because apparently it is easier to turn oil drillers into astronauts than the other way around.
That's completely ridiculous because it takes years to become a astronaut and less time to become oil drillers.
Another ridiculous thing is exploding a nuke on the surface. It wouldn't work because a asteroid the size of Texas is too big to even vaporize.
A better solution is to send a payload containing Tsar Bomba. The powerful nuke in existence.It is 3,000 times more powerful than the Hiroshima bomb.
Nuke near the asteroid to push it slightly so it's trajectory misses earth. There is nothing else we can do other than changing it's trajectory.