Granting citizenship rights to 700,000 Dreamers really means giving a foothold in the U.S. to perhaps 1.5 million other future immigrants, according to analysts who urged Congress to weigh the implications fully before pressing ahead with a mass legalization program.

Chain migration — the ability for the Dreamers to sponsor relatives, including their parents who broke the law by bringing them to the U.S. — is one of a number of issues President Trump and congressional leaders will have to work out as they reach for a deal on Deferred Action for Childhood Arrivals, the Obama-era amnesty that the administration is phasing out.

Mr. Trump and Democratic leaders suggested that they had settled on a broad framework Wednesday night, emerging from a dinner to say they would find a way to enshrine protections for those covered under DACA. But the more they talked, the more it became clear that they have yet to settle any of the thorny details.

House Minority Leader Nancy Pelosi, California Democrat, said Thursday that they agreed to start with the Dream Act, which is legislation to grant a full pathway to citizenship to illegal immigrants who came to the U.S. as minors, have kept a relatively clean record and are at least working toward a high school-level education.

Mr. Trump, though, said he is not interested in citizenship because it would amount to an amnesty.

Mrs. Pelosi also said the president agreed to forgo his demand for wall funding in the bill. Mr. Trump said that is true but he will need to see a down payment for the wall in other bills moving through Congress this year, or else he will throw a wrench in the works.

“The wall, to me, is vital. If I don’t get the wall, then we will become the obstructionists,” the president said.

Mr. Trump also said he needs “massive border security” and “extreme surveillance” to be part of the Dreamer deal. Those demands seemingly conflict with Mrs. Pelosi’s statement, which mentioned sensors, drones and access roads as the kinds of the border security measures she has in mind.

Those are just some of the issues to be worked out as Congress rushes against a six-month deadline Mr. Trump set last week when he announced the phaseout of DACA.

The Dreamers are considered the most sympathetic figures in the immigration debate. They often were brought to the U.S. as young children by relatives who left them no say in the decision. Many of them speak only English and have no ties to their birth countries, yet under existing law are expected to be deported if caught by immigration agents.

But granting them citizenship, as Mrs. Pelosi calls for, would mean they could eventually sponsor their relatives, including the parents who broke the law to bring them to the U.S.

Think tanks that study immigration said there is no concrete calculation of how many people Dreamers could sponsor, but estimates generally say each new citizen results in an average of one to two others.

“You would expect that each Dreamer or each DACA recipient in the long run would result in around two or three additional people,” said Steven A. Camarota, research director at the Center for Immigration Studies.

Constraints include per-country caps. Some applicants in the lowest-preference family category face a nearly 13-year wait before they are able to claim visas to immigrate to the U.S.

Much depends on who qualifies for the deportation amnesty Congress writes. If it’s limited to the approximately 700,000 people protected by the Obama-era DACA, then the chain of migration could be limited. Many of them already have siblings either as U.S. citizens or also protected by DACA who wouldn’t need to be sponsored.

If the legalization is similar to the Dream Act legislation introduced by Sen. Lindsey Graham, South Carolina Republican, and Sen. Richard J. Durbin, Illinois Democrat, then the total number of immigrants legalized could run closer to 2 million and the chain of migration could mean millions more eventual citizens.

Under existing rules, citizens can immediately sponsor parents, spouses and unmarried children younger than 18. Brothers and sisters and married or adult children have to wait in the backlog.

Mr. Durbin acknowledged Thursday that his bill, as written, would allow Dreamers to sponsor the full panoply of relatives, just as any other naturalized citizen can do.

“We have not addressed any exceptions to that rule in the Dream Act as currently written,” he said.

Mr. Graham agreed that was the way the bill was written, though he said he would like controls on chain migration. “Yes, we will have to deal with that issue,” he said.

He and Mr. Durbin also will have to grapple with how tightly to draw the net for legal status qualifications.

Under their current bill, illegal immigrants who came to the U.S. in the early part of the Obama-era Unaccompanied Alien Children surge could qualify, even though they explicitly came without their parents.

Mr. Graham said he would have to think about that situation.

“That is a good question. If they weren’t brought by their parents, it would be a different deal,” he said.

Some Republicans have suggested coupling the Dream Act with legislation sponsored by Sen. Tom Cotton, Arkansas Republican, and Sen. David Perdue, Georgia Republican, which would substantially limit family migration and would add a point-based system for selecting employment-based migrants.

Others have said they would like more measures to head off another wave of illegal immigration, such as mandatory use of E-Verify, the government’s electronic worker verification system that is currently voluntary for most businesses.