You asked what has Cruz done regarding illegals.....
Cruz names securing the border and stopping illegal amnesty among his top priorities.
....Cruz introduced legislation blocking President Obama’s expansion of the Deferred Action for Childhood Arrivals Program. (GovTrack)
....Cruz introduced the Protect Children and Families Through the Rule of Law Act which would prevent the expansion of the Deferred Action for Childhood Arrivals program; reform the William Wilberforce Trafficking Victims Protection Reauthorization Act so unaccompanied minors can be expeditiously united with their families back home; and take steps to ensure that state and local officials have the resources necessary to protect the people in their communities and secure the border. (GovTrack)
....Cruz led the opposition to the Gang of Eight amnesty bill in the Senate Judiciary Committee (Senate.gov) and voted against advancing the bill. (Senate.gov)
After the president’s 2014 executive amnesty Cruz was one of the few Republicans to speak out about Republican’s need to keep their campaign promise. (Breitbart)
....During debate over a spending bill at the end of the 113th Congress’ Lame Duck session, Senators Cruz and Lee took to the floor of the Senate calling for a vote on President Obama’s illegal executive action on immigration. Cruz’s and Lee’s proposal did receive a vote, losing twenty Republicans in a 22-74 defeat. (Politico)
.....Cruz was one the primary opponents to Loretta Lynch’s nomination. Not only did Cruz vote no on the important procedural vote to move the nomination forward, but he also actively took to the floor leading opposition. (Politico) (Senate.gov)
Cruz offered an amendment to the bill that only changed giving citizenship to the illegals. He supported their legalization.
Cruz Tries to Claim the Middle Ground on Immigration
What Mr. Cruz has tried to articulate in both word and deed is a middle ground. It got no support from Democrats in Washington, but it goes further than many on the far right want to go by offering leniency to undocumented immigrants here already: A path to legal status, but not to citizenship. A green card with no right to naturalization.
“The amendment that I introduced removed the path to citizenship, but it did not change the underlying work permit from the Gang of Eight,” he said during a recent visit to El Paso. Mr. Cruz also noted that he had not called for deportation or, as Mitt Romney famously advocated, self-deportation. Mr. Cruz said recent polling indicated that people outside Washington support some reform, including legal status without citizenship. He said he was against naturalization because it rewarded lawbreakers and was unfair to legal immigrants. It also perpetuates illegal crossings, he added.
Besides barring citizenship while instituting some level of legalization for those here already, Mr. Cruz has proposed increasing the number of green cards awarded annually, to 1.35 million from 675,000. He also wants to eliminate the per-country limit that he said left applicants from countries like Mexico, China and India hamstrung when they tried to gain legal entry to this country.
What did Cruz do about border security or a plan to track and deport visa overstays. Any legislation?