Work Permit after LMIA

Is it possible to visit Canada and find a job and then get a work permit?
How long does it take to get a work permit after the employer has done an LMIA?

Yeah you can ‘visit’ on a visitor visa and search for jobs and if successful get the company to apply for work permit. But I have heard that unless you have professional or personal contacts in companies or some extra ordinary skill that can be proved, its very difficult to convince a company to give you (a random stranger) an offer and do the paper work.

As for duration (my example and few posts in forums)
LMIA: best case 2 months, usually 2-5 months because of lawyer/company messing up
WP after LMIA: best case 1-2 months, usually 2-4 months