The plan proposes a number of changes to the legal immigration system, including a halt to any increases in legal immigration while "American unemployment remains unacceptably high," an end to public assistance for immigrant households, and a new system of prioritizing legal immigrants that takes into account things like language skills and education.

Cruz also called for a suspension of the H1B visa program for six months while it was audited, while proposing other changes to the program, such as an advanced degree requirement. Rubio had previously pointed to Cruz's support of raising the cap on H1B visas as proof the two were not so different on immigration.

Cruz's plan doesn't address how he would deal with the 11 million immigrants currently in the country illegally. Like the 2012 GOP nominee, former Massachusetts Gov. Mitt Romney, who favored "self-deportation," Cruz seeks to make life so tough for undocumented immigrants they would leave on their own; Cruz's plan, for instance, called for a ban on government benefits for undocumented immigrants.

"In the Senate, I have stood consistently with the majority of Americans against amnesty and lawlessness, and I will do the same as President," his plan, posted to his campaign website, said. "I give you my solemn word that, if I am elected President, we will use that authority to secure the border, and to restore the value of American citizenship and the Rule of Law."

The Texan senator also said he would make a federal crime overstaying the expiration of one's visa.

Additionally, the plan attacked the Obama administration policy accepting Syrian refugees.

"Instead, we should prioritize refugee status for religious minorities, especially Christians, Jews, and others being systematically tortured and murdered by radical Islamists in Iraq and Syria today," he said.