While the issue routinely comes up in talks between foreign leaders and the executive branch, embassy officials are ramping up their outreach to Congress and the White House in order to take advantage of the best hope for reform in years.

A number of countries with significant immigration ties to the United States — notably Mexico, Ireland and several Central American nations — have been making their concerns known while doing their best to avoid meddling in domestic affairs.

For many countries, the issue goes beyond humanitarian concern: Remittances from foreign nationals living in the U.S. provide a significant boost to the economies of their home countries.