1. Allow the federal government to cut off money transfers (aka remittances) from illegal immigrants back to their relatives, friends, and associates in Mexico.
2. Impose trade tariffs with Mexico.
3. Increasing immigration visa fees from Mexico, including fees on border crossing cards, of which more than 1 million are issued a year.
4. Use all drug money and property seized from cartels and others involved in illegal drug trafficking both in the United States and in Mexico. Law enforcement and National Guard could work together through joint operations. $8.7 billion was seized by the U.S. Justice Dept. in 2015 alone. Add in similar assets seized by Mexico depositing said assets into a “joint border security fund,” from which funding for the construction and ongoing maintenance of the wall could be paid for.
All valid, reasonable methods of raising the funds with a minimum of additional cost or effort required. It also has the added bonus of negatively impacting many of those who would abuse the privilege of visiting the United States.
Gangs, drug / human traffickers, and cartels have freely exploited our open borders and committed crimes inside the United States. We have borne the extraordinary daily cost of this criminal activity, including the cost of trials and incarcerations. Not to mention the greater human cost.
A combined, cooperative effort to boost border enforcement might bring significant economic, national security, as well as health and safety benefits to millions of citizens in both nations.
Mexico probably benefits more from illegal immigration — i.e., relocating many poor and/or criminals to the U.S. and getting an influx of cash from the remittances — than if they kept those people in Mexico.
Mexican officials are probably also pressured / threatened by the cartels to block any efforts that would put a serious dent in their bottom line.
More progress could be accomplished through combined efforts from both governments and with the public support of the citizens of both countries.