The Post-ABC survey finds 86 percent support for dreamers who had been eligible for renewable two-year work permits under a deferred action program started by President Barack Obama to remain in the country. Trump's administration announced this month that it will end the program, known as Deferred Action for Childhood Arrivals, and begin to phase out work permits in March if lawmakers do not act.
About 690,000 immigrants are covered by DACA status, according to the Department of Homeland Security, although Democrats are likely to seek protections for a significantly higher number.
More than two-thirds of adults — 69 percent — support the DACA program "strongly," which was described as allowing undocumented immigrants to stay in the United States if they had arrived as a child, had completed high school or served in the military and had not committed a serious crime. In a follow-up question, 65 percent back a law that would both allow dreamers to remain in the country and increase funding for border security. The poll did not measure public opinion about whether the dreamers should be offered a path to citizenship, a prospect GOP immigration hawks have called amnesty.
Trump and his aides have offered mixed signals on a deal. The president met with Senate Minority Leader Charles E. Schumer (D-N.Y.) and House Minority Leader Nancy Pelosi (D-Calif.) this month and agreed to pursue a deal for the dreamers. Democratic aides said the deal would be based on the "Dream Act," a bipartisan proposal that offers a path to citizenship.
But Trump said two weeks ago on a trip to Florida that "we're not looking at citizenship. We're not looking at amnesty. We're looking at allowing people to stay here. . . . We're talking about taking care of people, people who were brought here, people who've done a good job."
The president added that any deal is contingent on including "extreme security" measures in terms of immigration enforcement, suggesting he envisioned at a minimum increased "surveillance" along the border. He also pledged to continue pushing for funding for a costly wall along the U.S.-Mexico border, which Democratic lawmakers and some moderate Republicans oppose.
Trump has said he will not demand that money for the wall is included in a dreamer bill but insisted the wall would have to be funded somehow. "If there's not a wall, we're doing nothing," he said.
The Post-ABC poll shows significant opposition to a wall. Roughly 6 in 10 continue to oppose the building of a barrier, which Trump made a centerpiece of his campaign, with attitudes little changed over the past year.
Trump also has suggested he would seek cuts to legal immigration in pursuing a deal for the dreamers. Republican Sens. Tom Cotton (Ark.) and David Perdue (Ga.) have proposed legislation called the Raise Act, which Trump has endorsed, that would slash the rate of legal immigration by half over a decade. Currently, more than 1 million foreigners each year receive green cards allowing them permanent legal status in the United States.
The survey finds that 55 percent oppose massive immigration cuts, which also are strongly opposed by business leaders.
An alternative border security concept draws higher marks from the public. A lopsided 79 percent supports requiring employers to verify that all new hires are living in the United States legally, including 61 percent who support such a requirement strongly.
The concept of using a computer database to force employers to vet the immigration status of their workers, under a program called E-Verify offered by U.S. Citizenship and Immigration Services, has been included in previous immigration reform bills. But the program has not been universally implemented.
Conservative Republicans and immigration hawks, including conservative talk show hosts and restrictionist groups, support the expansion of the E-Verify program.
Mark Krikorian, executive director of the Center for Immigration Studies, which advocates stricter immigration limits, has proposed coupling legal status for dreamers with cuts to legal immigration and the mandatory use of E-Verify by businesses.
"E-Verify already exists; last year, around half of new hires were screened through it," he wrote last month in National Review. "Rolling it out for the other half is something that would happen at the same time as the amnesty."
Trump's willingness to bargain with Democrats over his signature campaign issue has alarmed immigration hard-liners, who fear he is softening in hopes of scoring a legislative victory in a first year marked by stumbles and defeats on Capitol Hill.
At the same time, liberals and moderates believe Trump has been too draconian in his travel ban on immigrants and refugees from some majority-Muslim countries and his executive actions that have expanded the pool of undocumented immigrants who are targets for removal.
In all, 62 percent of Americans disapprove of Trump's handling of immigration matters. When asked about immigration enforcement, 49 percent of Americans believe enforcement was not tough enough under Obama, while 44 percent said it was just right and 6 percent say it was too tough.
Under Trump, 30 percent say enforcement levels are about right and 45 percent say they are too tough, seven times higher than before he entered office. Just about half of that — 22 percent — say immigration enforcement is still not tough enough under Trump.
Though Trump has railed against the dangers of illegal immigration, and has met with victims of crimes in the Oval Office and at campaign events, most Americans have not embraced Trump's association of immigration with increased crime. Some 12 percent of the public say undocumented immigrants commit more crimes than other people in the country, while 19 percent say they commit fewer crimes. Sixty-four percent say there is no difference, while the rest have no opinion.
The Washington Post-ABC News poll was conducted Sept. 18-21 among a random national sample of 1,002 adults reached on cellular and landline phones. Overall results carrying a plus or minus 3.5-point margin of sampling error.
Emily Guskin contributed to this report.