With the current "shortage", how hard is it to get a job as a Programmer?

I'd say that there is a programmer shortage, but there may be a gap between employer and employee expectations. Note that Fizz-Buzz isn't so much a confirmation of a hire, but a simple filter against people you don't want to hire. Passing it just means you're eligible for an onsite interview at a company good enough to use it as a filter, not necessarily that you'd get hired. One of the challenges for a new grad or engineers without a lot of experience is that, more and more, companies expect their hires to have some form of programming ability beyond what they did in school. With so many online resources available and so many candidates coming up with their own projects, it's hard to come out of school or even from a job (where the technology used is not hot/popular/impressive) without a lot of side projects and other initiatives and get noticed. A "junior" position will still need these extracurricular activities. The other possibility is that you're picky enough to not apply for companies that don't sound that attractive, and so you are implicitly competing with the hot companies which attract all the top candidates. On the plus side, with a higher bar, companies will also pay more and start their junior hires with higher salaries.

In North America there seem s to be a high demand for Java developers because they are considered all-rounders. Java supports web, mobile applications and is object oriented. Do a search on http://indeed.com for key terms and other job boards to see what is being sought and take it from there.

It also depends  on how much you want to make.   The market for senior talent is somewhat slow right now.  A lot of people seem to be "bargin hunting" because of the over-all economy.

If you don't have paid experience forget about getting a job. That's the filter.

It really depends on your location and field of knowledge. For example, if you develop RoR applications, and live in Silicon Valley, you'll find a new job in no time. I can't really give a detailed answer because you didn't address specifics, but I hope this helps a little bit.