What should I do with a guy, who rejected help, promised to do the work and just didn't even try to do it?

Everything within your power to ruin him would be my answer. But I'm kind of a bastard. Proceed with caution if you take my advice.

I can understand them wanting to do it themselves as I am the same. However if you are unable to find a solution in a reasonable amount of time, you should really ask for help.

All i can say is do what you think is right

@hackedranger several iterations of bugfixing will do the job :)

@nblackburn it's not a deadline problem, it's motivation problem - I've done it in a half of a day ( and i needed to deep dive into it ). This guy is rather experinced to do it in reasonable amount of time.

Tough question. Throwing someone under the bus is usually not good. Try to advise the person. PM or management should begin to notice if they are competent.
Document everything you ask the person to do and delivery dates. It will be useful down the road.