One word defined the immigration debate under former Presidents George W. Bush and Barack Obama: amnesty. Under President Trump, it might be two: chain migration.

“Our current immigration system fails Americans,” Trump said at the White House on Thursday “Chain migration is a total disaster, which threatens our security and our economy and provides a gateway for terrorism.”

Trump said it again when spelling out what would have to be in a bill to codify the Deferred Action for Childhood Arrivals program, ending in March, in order for him to sign it. DACA protects undocumented immigrants who arrived in the U.S. as minors from deportation. Because Obama created it through executive action, there are questions about its legal and constitutional basis. Attorney General Jeff Sessions announced in September that the program would be phased out for these reasons.

“Any legislation on DACA must secure the border with a wall,” Trump remarked after meeting with Republican senators on the issue. “It must give our immigration officers the resources they need to stop illegal immigration and also to stop visa overstays. And, crucially, the legislation must end chain migration. It must end the visa lottery.”

White House press secretary Sarah Sanders described the president as reiterating in the meeting with GOP senators the administration’s “view that any action on DACA must come with action on the president's immigration reform principles, which were released last year.”

“These include a physical border wall on the southern border; interior enforcement, which includes more ICE and Border Patrol agents; as well as a crackdown on sanctuary cities; and reforms to our legal immigration system, like ending chain migration and the visa lottery program in favor of a merit-based immigration system,” Sanders said at Thursday’s press briefing.

“Next week, the president is inviting a bipartisan group of senators to the White House to discuss next steps on responsible immigration reform and to continue that discussion,” she added.

“Chain migration” is a phrase used to describe a feature of immigration law that allows immigrants to sponsor their relatives to come to the U.S. Family reunification is responsible for more than two-thirds of legal immigration annually, while less than 10 percent come for primarily employment-based reasons.

Immigration restrictionist argue this produces a mismatch between immigrant skill levels and the U.S. labor force, at the expense of American workers and recent immigrants.

A bill introduced by Sens. Tom Cotton, R-Ark., and David Perdue, R-Ga., endorsed by Trump in August, would cut immigration in half in part by limiting family-based immigrant sponsorship to spouses and minor children. They would like to see something like this provision be part of any DACA deal.

“Look, if you give amnesty to one or two million illegal immigrants who were brought here through no fault of their own, as kids, you’re going to have at least a couple negative effects,” Cotton said on Fox News. “And one of those negative effects is you’re going to have a whole new chain of chain migration. The way to control for that negative effect is to stop chain migration.”

The immigration hawks at Numbers USA have launched a six-figure ad campaign to inform the public and to help the phrase "chain migration" take its place in the political lexicon alongside "amnesty." The group’s president, Roy Beck, uses the words together.

“While Congress debates yet another amnesty, we want to help Americans visualize how the presence of chain migration categories means that amnesties are never limited to the people receiving them but instead open up lifetime work permits to millions more of their extended family and in-laws,” Beck said in a statement.

Many of the Republicans negotiating with Senate Democrats on a DACA fix favor more expansive immigration policies than Trump. Sen. Lindsey Graham, R-S.C., for example, was part of the Gang of Eight and is a co-sponsor of the Democrats’ preferred bill for resolving the status of DACA.

Social conservatives helped beat back a 1990s attempt to reduce immigration in part by limiting chain migration on the grounds that family reunification was a pro-family policy. Many immigrant communities and their advocates also oppose the change, arguing that it is already too difficult to immigrate to the U.S. and, this is, itself, a driver of illegal immigration.

But Graham suggested Thursday that Trump could succeed where Obama and Bush failed if lawmakers were willing to compromise. “There's a bill to be had,” he said at the White House. “If you want it bad enough, we'll get it and it will be good for the country. Everybody has got to give a little bit. But I've never been more optimistic about an immigration reform proposal making it to the president's desk right now.”

Sen. Jeff Flake, R-Ariz., has been a persistent critic of Trump on immigration, among other issues, and asked for a place at the table on DACA negotiations when the administration was lobbying him on tax reform. Still, Flake tweeted in December that he could make some concessions the White House wanted, specifically mentioning chain migration.

“We can fix DACA in a way that beefs up border security, stops chain migration for the DREAMers, and addresses the unfairness of the diversity lottery,” he wrote. “If POTUS wants to protect these kids, we want to help him keep that promise.”

Trump has held to these positions even after his split Steve Bannon, who pushed for immigration restrictions when he was working at the White House and has published numerous articles on the subject on his media site Breitbart.

Pressure is building to craft a legislative solution for DACA, as beneficiaries’ work permits are starting to expire and there are concerns about how long it would take to ramp up the program again if Congress authorized its revival.

“We must BUILD THE WALL, stop illegal immigration, end chain migration [and] cancel the visa lottery,” Trump tweeted Thursday evening. “The current system is unsafe [and] unfair to the great people of our country — time for change!”