Q. Can an individual get a Canadian GC and continue work in US and also apply for US Permanent residency? if so by what time has one to decide which one he or she should stick with ?

Answer: There is no bar to applying for permanent resident status in either Canada or the USA while holding similar status in the other country. You may not legally maintain such status in both countries indefinitely, however. The time at which the decision would have to be made is theoretically at the time of landing at the second country, although in practicality it can often be deferred.