Objects the size of Texas cannot be diverted.
As far as an object of up to perhaps 10 km in diameter, diversion is possible by nuke. No rocket motor that we can possibly put into an asteroid (with any foreseeable extension of present technology) could produce the delta-V of a single 10 megaton nuke, no matter how long it managed to operate.
Frankly, I don't see a 10 megaton nuke breaking up a 10 km asteroid. It just doesn't have sufficient energy to do that, IMHO. It will just vaporize a modest size crater whose vapors will give the asteroid a tiny shove, with a delta-V of no more than 1 m/sec or so, if we are lucky. However, 1 m/sec is plenty of delta-V provided that we have several years of advance notice and calculate correctly.
David F Mayer