If I'm not mistaken Visa's are generally obtained to work in the United States, so a similar program already exists. I do believe it is feasible and practical to allow this to happen, but the truth is, is that for the most part America does not have jobs to offer people from outside of the country. America, at best, would need professionals, like doctors.
I see no problem with churches charging their members, particularly those members with the financial ability to pay. Churches have basic needs to pay staff, energy costs, and building maintenance, and should seek money from the congregation to pay for those. Of course, no one who cannot afford to pay should be turned away.