The immigration bill — which is expected to pass by the end of the week — would grant nearly 11 million illegal immigrants provisional legal status for 10 years before they could then apply for a green card. 

At the insistence of Sen. Orrin HatchOrrin Grant HatchOvernight Finance: NAFTA defenders dig in | Tech pushes Treasury to fight EU on taxes | AT&T faces setback in merger trial | Dems make new case against Trump tax law | Trump fuels fight over gas tax What sort of senator will Mitt Romney be? Not a backbencher, even day one Lawmaker interest in NAFTA intensifies amid Trump moves MORE (R-Utah), immigrants would not be eligible for ObamaCare benefits in addition to other mean-tested welfare until after they've gained citizenship.

"What has this nation come to? It’s getting harder and harder to recognize America," Cruz said. "We're now considering a law that is thinly disguised as human trafficking."

Cruz said the bill creates a “$5,000 amnesty tax” for employers, causing them to fire U.S. employees and hire immigrants to avoid paying the penalty. He added that if this bill passes, unemployment for minorities and legal immigrants will increase.

The bipartisan group of eight senators, known as the Gang of Eight, introduced S. 744, which would create a pathway to citizenship for illegal immigrants already in the country, toughen border security, create a guest worker program and boost high-skilled immigration.

Cruz asked to call up his amendment, but Democrats objected. Cruz said his amendment would have defunded the Affordable Care Act, also known as ObamaCare, until no more immigrants had RPI status — which would be at least 10 years.