A top aide to President Trump signaled Tuesday that the White House may back off its calls to pair funding for new U.S.-Mexico border wall construction with a bill to provide legal protection to hundreds of thousands of immigrants known as "dreamers," signaling that the emotionally charged issue may prove easier to resolve than initially thought.

Trump last month sparked a six-month countdown to the end of the Deferred Action for Childhood Arrivals (DACA) program, which legally protects about 690,000 people, saying that it is up to lawmakers to come up with a solution. The decision has been widely criticized by members of both parties and the issue has quickly become a top-of-mind concern across Washington.

Marc Short, the White House legislative affairs director, told a breakfast gathering held by the Christian Science Monitor on Tuesday that Trump "believes that a physical barrier is important" between the United States and Mexico. But he said that the administration does not "want to bind ourselves into a construct that makes reaching a conclusion on DACA impossible."

Short's comments came as House Minority Leader Nancy Pelosi (D-Calif.) signaled that House Democrats are quickly coalescing around legislation that would grant legal protection to DACA recipients and set them on a years-long course to apply for U.S. citizenship. The Dream Act is co-sponsored by Democrats and Republicans in the House and the Senate, including Reps. Lucille Roybal-Allard (D-Calif.) and Mike Coffman (R-Colo.); Sens. Jeff Flake (R-Ariz.), Lindsey O. Graham (R-S.C.) and Richard J. Durbin (D-Ill.); and Senate Minority Leader Charles E. Schumer (D-N.Y.).

Pelosi said Tuesday that House Democrats are gathering support for a petition to force House Speaker Paul D. Ryan (R-Wis.) to hold a vote on that legislation as early as the first weeks of October. For such a strategy to succeed, Pelosi would have to obtain signatures from every Democrat in the House and at least 24 Republicans.

Pelosi said Tuesday that Democrats should act quickly to take advantage of a moment when there appears to be widespread public support for extending legal protection for those covered under DACA.

"Public opinion is very hot," she said in an interview. "We have to strike while the iron is hot."

Several recent polls have shown that a majority of voters support extending legal protection to DACA recipients in the wake of Trump's decision to end the program. A recent NBC News/SurveyMonkey poll found that 64 percent of respondents support DACA, including 85 percent of Democrats, 41 percent of Republicans and 66 percent of independents. Less than one-third — 30 percent — of all respondents said they oppose the program.

But the issue of border wall funding is still likely to be a point of contention in spending negotiations later this year. Congress voted last week to extend current spending levels through Dec. 8, leaving lawmakers three months to work out a long-term spending agreement. Short hinted Tuesday that Trump may demand border funding as a part of those negotiations.

"The president is committed to sticking by his commitment that a physical structure is what is needed to help protect the American people. Whether or not that is specifically part of a DACA package or a different legislative package, I am not going to prejudge. But he is committed to making sure that the wall is built," Short added.

In recent days, Trump also has privately approached Schumer to discuss trading protections for DACA recipients in exchange for new border wall funding, said a person familiar with their exchange who wasn't authorized to speak publicly on the matter.

Congressional Democrats have said they will not discuss any deal involving new money for border wall construction, but are open to discussing broader border security measures. In a 2013 bipartisan immigration reform bill, Schumer and dozens of other Democrats supported billions of dollars in new funding to hire U.S. Border Patrol agents, and to deploy drones and other technology to scan and protect the southern border — proposals that are still considered viable, aides have said.

But Schumer, Pelosi and other Democrats have called construction of more border wall "immoral" and a misguided use of federal money, especially at a time when the federal government needs to spend hundreds of billions of dollars in relief aid to rebuild parts of Florida, Texas and Louisiana after recent major hurricanes.

Trump promised during a White House meeting last week that he would sign the Dream Act if it passes Congress, Pelosi said. Democrats have generally been skeptical of trusting Trump's word on policy matters, but Pelosi said she is certain he will follow through on the pledge once it is clear that Congress has the votes to pass something.

"We have to have the votes to pass the bill," Pelosi said. "Votes are the currency of the realm."