By Caitlin Ostroff, Ciara Bri'd Frisbie and Alice Kantor, CNN

(CNN) -- A bill to slash legal immigration won President Donald Trump's support on the belief that it would help Americans making low wages.

CNN took a look at the claims made by Trump and the bill's authors.

Claim: Our immigration program is based mostly on family connections.

This is true. So far this year, about two-thirds of immigrants are given green cards because they have family members in the United States, according to the Department of Homeland Security.

Claim: Only one in 15 immigrants come to the US because of job skills.

One of the authors of the bill, Arkansas Sen. Tom Cotton said, "Only one in 15 out of a million new immigrants come here because of their job skills and their ability to succeed in this economy."

In fact, about one in seven immigrants in the first half of fiscal 2017 were granted green cards related to jobs, according to the Department of Homeland Security. This includes many immigrants who are singled out for having advanced skills or being professionals.

The high number of family-related green cards doesn't mean, however, that those immigrants don't have skills, said Doris Meissner of the Migration Policy Institute, an immigration think tank.

A report by her group found that while 16% of workers in 2014 were immigrants, they made up a third of all computer scientists, 30% of health-care professionals and 26% of physicians or dentists.

College-educated immigrants, however, are more likely to be underemployed, according to the Migration Policy Institute. From 2012 to 2014, about 23% of immigrants with a college degree were working low-skilled jobs as dishwashers, security guards and taxi drivers.

Claim: More than 50% of all immigrant households receive welfare benefits.

A White House statement says "more than 50% of all immigrant households receive welfare benefits."

This echoes research from the anti-immigration group, Center for Immigration Studies. But that group includes both legal and illegal immigration in its calculations. The White House has cited no source for this claim.

Immigrants are not eligible for many welfare benefits for the first five years, according to Meissner. Congress changed the law in 1996 to deny new immigrants many benefits in that period.

Based on 2011 data, non-citizen immigrant adults and children are about 25% less likely to be signed up for Medicaid than native-born citizens and are 37% less likely to receive food stamps, according to a study by the Cato Institute.

Claim: Since 1979, Americans with a high school diploma or less have seen their real hourly wages decline.

This is true. In fact, real hourly wages have declined for most Americans. But few economists pin the blame on immigration.

Claim: The White House contends that "unskilled immigration into the United States has surged, depressing wages and harming America's most vulnerable citizens."

The effect of immigration on low-wage workers has been studied for years, with several studies suggesting that immigration has little effect on wages.

For instance, an economist at the University of California Davis, Giovanni Peri, found in 2015 that there is little evidence that immigrants depress wages for low-skilled workers.

Some economist contend that immigrants boost the economy by becoming consumers. A study from the University of Virginia found that for every job an immigrant has, 1.2 jobs are created.

Claim: Cutting green cards by 50 percent annually returns immigration to historical norms.

This is a point made by Cotton. In reality, immigration has been higher in the past, including several years around the turn of the 20th Century. For instance, there were nearly 1.3 million immigrants in 1907, about a quarter of a million more than in 2015.

Immigration relative to the US population peaked in 1890, when immigrants made up nearly 15% of the population, according to the Migration Policy Institute.