The Department of Homeland Security also announced it will no longer scoop up undocumented immigrants arrested for minor offenses such as traffic tickets, and that it is phasing out a controversial but popular program, known as 287(g), which granted police and sheriff’s deputies the power to start the deportation process on arrested illegal immigrants.

Reaction around the country has been mixed. Many undocumented immigrants, like 25-year-old Sandra Tovar of Forth Worth, are trying to be optimistic, but they also are wary.

Tovar, who recently received deferred action on deportation, remembers the multiple failed efforts to overhaul immigration law. The consequences included a wave of anti-illegal immigrant sentiment in local communities.

States such as Arizona, Alabama and Georgia implemented their own strong immigration laws geared toward encouraging undocumented immigrants to leave. Several more communities in Texas, Florida and North Carolina, among others, joined the 287(g) program. According to U.S. Immigration and Customs Enforcement, nearly 60 local law enforcement agencies in 21 states operated the program.

On a recent evening, Tovar joined other advocates in strategy sessions at the Catholic Men’s Club in north Fort Worth, near the historic Stockyards, which is home to long-established Mexican-American families.

“There’s still that feeling of not knowing what is going to happen and being afraid,” she said at the club Thursday. “We know it can be everything or nothing.”

Anticipation is growing at the Kansas City, Mo.-based Don Bosco Center, which offers immigrants and refugees free English classes. At the center, news of Obama’s policy changes for immigrant families has spread slowly from “cousin to cousin,” according to David Holsclaw, director of the English as a second language program.

Pedro Ramirez, the 24-year-old son of farm workers in Fresno, Calif., got a hug from his mom when he told her this month that he was granted deferred action and a work permit – and that his U.S.-born brother could one day sponsor the rest of the family to gain their residency status.

“I kind of sprung both surprises on both of them,” Ramirez said. “You wouldn’t believe how many families have mixed status.”

The White House appears to be testing the public’s temperament on immigration by rolling out changes that, just a few years ago, would have been more strongly opposed, said Susan Gonzalez Baker, director for the Center for Mexican American Studies at The University of Texas at Arlington.

“It allows the administration to implement some policies that demonstrate the world is not going to end if immigration reform includes benefits, not just walls and more enforcement,” she said.

The highest hurdle to any agreement will likely be in the House of Representatives. The Republican-controlled House has long been resistant to a comprehensive plan. Leaders on this issue, such as Rep. Raul Labrador of Idaho, a tea party-backed member and Puerto Rico native, have instead called for a more piecemeal approach.

Labrador on Monday questioned whether the Democrats wanted a political victory or a policy victory. Democrats can’t just “draw a line in the sand” and refuse to compromise and then blame Republicans if it fails, he said in an interview.