We actually already tax immigrants more than citizens. They pay the same taxes we do but don't qualify for all the deductions, and pay into social security and medicare even though they can't get those benefits.
As an American I do not qualify for either of those things but have to pay into it, you need to pay into the system for 40 quarters (10 years), and meet other requirements. It is currently underfunded and most likely wont have much money left by the time I could withdraw. If you have a higher income and/or a spouse that works you generally pay in more than you will get back in benefits as well because it is a progressive safety net system. I've seen many people see the high salaries and the good quality of living in the US, but many of these things take high taxes to pay for.
I guess the idea would be that the employers are taxed, not the employee. Also, H1Bs are already taxed all the regular taxes even if they return to their country before they could use Medicare or gather enough SS credits.
People have a choice of where they want to go for work. If you tax them so hard that anywhere else is better then you may as well have simply not bothered pretending like you wanted it to be easier for them to come at all.