Getting an FAA certificate is simple enough. Getting employed by a US carrier is a different story. There are too many unemployed or under-employed US pilots. The US regionals claim a shortage of pilots, but what they actually have is a shortage of qualified pilots willing to work for minimum wage. (I've heard of guys opting to fly a PC-12 over a CRJ because the money was so much better.) Since the H1B visa process costs the employer money (as far as I know), I would be interested to find out if a US regional is willing to go that route rather than offer more money to a qualified American pilot. I have my doubts, because even if the airline was willing, it is very unlikely that USCIS will approve the visa.
The Aussie thing (for those that are wondering) is due to a Bush (the son) Administration era work-exchange set-up, where a certain number of pilots from each country can get work authorization to go to the other country per year. That has apparently been gaining some traction recently with US regionals.
If any foreign pilots (of whatever nationality and whatever experience level) have gotten hired by any US airline or Part 135 charter operator, please post here - I would love to be proved wrong.