It would provide a pathway to citizenship for 1.8 million young people who came to the United States illegally as children in exchange for $25 million in border security funding and new limits to chain migration.
Senate Majority Leader Mitch McConnell, R-Ky., backs the Trump plan, which has been introduced in the Senate by Sens.
The provision to limit chain migration, which Democrats call family reunification, is the main sticking point, Graham said.
Democrats oppose the GOP plan to limit chain migration to nuclear families, comprised of minor children and spouses.
“We continue to believe a narrow proposal has the best chance of passing the Senate and the best chance of being signed into law,” Senate Minority Leader Chuck Schumer, D-N.Y., said Tuesday after meeting with party lawmakers privately.