I do support unlimited H1B visas, and I would also want to liberalize H1B visas even more. I think that, because it's hard for a worker with a H1B visa to start their own company or to move between companies, the company that is sponsoring the H1B has more negotiating power. (i.e. "well if you don't work hard enough, we can effectively have you deported") and are thus able to exploit their workers more. The limitations I would want on borders are checks for criminal background, and some kind of verification that the people immigrating understand liberal democracy and civil liberties and want to share in that system.
So, there's this idea of comparative advantage. Two companies are both producing widgets, but for some reason one company can produce goods cheaper than the other. The reasons might be things like technology, company or regional culture, training of employees, cost of resources, or geography. If no trade is allowed, then the company with the comparative example can only operate within it's own region. If trade is allowed, then everyone gets the benefit of the cheaper product. Furthermore, the economy is more efficient now!
An example: If it costs Company A $2 to make a widget, and it costs Company B $3 to make a widget, then trading will lower the price. Company B may still be able to be in business, but consumers will get the benefit of competition between the two and having lower prices. Furthermore, because Company A probably selling more widgets now that we've allow trade, the economy is also more efficient, because we're spending less money just producing widgets.
The idea that trade is beneficial is widely accepted. ( http://www.igmchicago.org/surveys/free-trade ) Protectionism is just one example of an anti-trade policy, so it follows that protectionism is bad, inefficient, and a tradeoff in which there are a few local winners, but at the cost of global efficiency, and as a direct tax on the people living in the region that's "protected".
Khan Academy on trade & comparative advantage: https://www.khanacademy.org/economics-finance-domain/microec...
A longer essay about the topic, which addresses the common arguments for protectionism (i.e. infant industries, spillover effects, national security, unequal exchange): http://www.e-ir.info/2012/08/28/the-causes-and-effects-of-ec...