In order to get PR, they would require you to undergo a medical exam by a designated physician. They'll ask you a lot of questions and do some tests. I don't know if cancer is an automatic disqualifier, but it might be. The essential question they have to determine (per the medical guide) is whether, in the next ten years, you will require more than your fair share of medical attention. If your cancer is in clear remission and it's of a type that tends to stay in remission, I can see how they might pass you. But it's gray area.
re: work permit..
If you're offered a job in Canada and your employer obtains the necessary approvals, you'll only need a medical examination if you've spent more than six months in one of the 'designated countries' in the year immediately preceding your entry date to Canada. Since the U.S. is not one of the designated countries, you'd have to intentionally go someplace else. So .. you probably won't need the medical. Here's a list of the designated countries.
http://www.cic.gc.ca/english/information/medical/medexams-temp.asp