What do you mean by Normal jobs? Obviously there is no shortage of accountants, HR resources, bankers or even mere IT resources in Canada.
To obtain LMIA an employer has to advertise a job for at least 4 weeks on CIC approved job portals and have to show that they tried recruiting Canadians first but couldn't find people of that skill set and as a last resort (these are the exact words in official description), they went on to recruit from outside of Canada.
It is not impossible, and happens often. The only question is - do you have any such skill? And it is not revolutionary, just a specific experience.
If you are in IT, and have specific experience in embedded development in multicore network processors, network function virtualization or SDN, Octeon / Broadcomm chips etc., send me a message. My employer regularly recruits people on LMIAs from all over the world.
If this sounds too hard, you should look at PNP options. They keep opening up on and off. Saskachewan has done that twice this year and their PNP conditions are met by people sitting out side Canada if their profession was in the list of needed ones, they had required funds, and were quick to apply in time (it was on a first come first serve basis if you qualify otherwise)
