According to a Morning Consult/Politico poll, Americans are generally in favor of having a more selective legal immigration system.
The poll showed that 62% support a system that gives English-speaking immigrants an advantage, and 61% support a point-based system to select employer-based immigrants.
54% also said that they want the government to look at an immigrant's need for taxpayer assistance in the decision process.
Cutting down the number of legal immigrants form 1.1 million a year to about 500,000 a year is a little more controversial, with 48% supporting it and 38% against it.
The new immigration bill, known as the RAISE Act, comes from Republican Senators Tom Cotton of Arkansas and David Perdue of Georgia.