The Trump Administration called for an end to the Visa Lottery and Chain Migration in its National Security Strategy released earlier today. The document mostly focuses on non-immigration-related national security issues, but does highlight the Visa Lottery and Chain Migration as being possible threats to national security and public safety.

In a section titled "Strengthen Border Control and Immigration Policy", the administration says that the nation's current legal immigration system does not serve the national interest and needs reforming.

"The United States recognizes that decisions about who to legally admit for residency, citizenship, or otherwise are among the most important a country has to make. The United States will continue to welcome lawful immigrants who do not pose a security threat and whose entry is consistent with the national interest, while at the same time enhancing the screening and vetting of travelers, closing dangerous loopholes, revising outdated laws, and eliminating easily exploited vulnerabilities. We will also reform our current immigration system, which, contrary to our national interest and national security, allows for randomized entry and extended-family chain migration. Residency and citizenship determinations should be based on individuals' merits and their ability to positively contribute to U.S. society, rather than chance or extended family connections." -- National Security Strategy of the United States, December 2017

The National Security Strategy also calls for strengthening border security and taking steps to curb illegal immigration. While it fails to mention requiring all employers to use E-Verify for all new hires to end the jobs magnet and reduce future illegal immigration, it does state that illegal immigration "burdens the economy" and "hurts American workers".

You can read the Trump administration's National Security Strategy at WhiteHouse.gov.