(CNN) Jeanette Vizguerra and Arturo Hernandez stood proud and free in the Denver sunshine on Friday and vowed to battle for their fellow undocumented immigrants.

The two, who had at times hunkered down in the same Denver church to elude deportation, celebrated being granted temporary stays of removal by Immigration and Customs Enforcement, their attorneys said. Both had lived in the country without proper documentation for more than a decade before separate encounters this year with ICE.

"It's a special day for me because I will be able to celebrate Mother's Day with my children and with my grandchildren," Vizguerra said. "It's been three months -- very difficult months."

Undocumented immigrant Jeanette Vizguerra stands with her family as she addresses supporters Friday in Denver.

Vizguerra's case -- and to a lesser degree Hernandez's -- have gained international attention as perceived examples of President Donald Trump's efforts to crack down on illegal immigration. Time magazine this year named Vizguerra one of its 100 Most Influential People in the world

Vizguerra and Hernandez, who both hail from Mexico, thanked cheering supporters -- including lawyers, clergy, activists and community members -- Friday at an outdoor news conference. They gave remarks in Spanish that were translated into English.

'My struggle is their struggle'

After learning of ICE's decision to let her stay through March 15, 2019, Vizguerra, who has three American-born children younger than 12, said she didn't know whether to laugh or cry.

"My hands were sweating," she said.

She vowed to continue fighting for immigration reform and for other undocumented people who are fighting to stay in the United States.

"My struggle is their struggle," she said. "The pain is my pain."

Vizguerra, who has been living in sanctuary churches for the past 86 days, will return to her family and to work as she awaits a response to her visa application, according to the Metro Denver Sanctuary Coalition.

"Jeanette belongs here," said Hans Meyer, Vizguerra's attorney, in what he cast as a message directed at Washington. He also praised her "unimaginable courage."

Hernandez also was granted a stay of removal, Meyer said. He "was recently released from ICE detention so he can attend his daughter's graduation," CNN affiliate KDVR reported

"I'm happy for myself and my family," Hernandez told supporters Friday. "Tomorrow we will continue supporting our fellow brothers and sisters that need us."

The stays will give Hernandez and Vizguerra time show ICE that they should be allowed to remain in the country legally, said Laura Lichter, Hernandez's lawyer. She slammed the Trump administration's immigration policy as unfair and an "absolute travesty."

"The question that should be asked: 'Why are people like Jeanette and Arturo facing deportation at all?'" Lichter said.

Immigration provisions tightened

Sen. Michael Bennet and Rep. Jared Polis -- Colorado Democrats who advocated for both undocumented immigrants -- hailed ICE's latest action both cases. The stays, Bennet said, will give both immigrants "more time to receive due process."

"This is also a reminder that there are many more families like theirs across the country experiencing similar fear and uncertainty," he said.

The lawmakers also had introduced so-called "private bills" on Vizguerra's behalf . The tactic aims to address a specific person's immigration status through legislation rather than through the ICE bureaucracy.

Immigration officials typically have delayed deportations while such bills are pending. But the Trump administration just reined in that allowance.

ICE announced last week that it is tightening its policy for granting "stays of removal in connection with private immigration bills," the agency's acting director, Thomas Homan wrote in a letter to Senate Judiciary Committee Chairman Charles Grassley, R-Iowa.

Such private bills, Homan explained, are designed to "confer lawful permanent resident status on beneficiaries by circumventing the normal immigration law framework."

ICE in the past has "routinely granted these stays" of deportation after getting investigative reports from the House or Senate judiciary chairs or the appropriate subcommittees on a person for whom a private bill has been introduced, Homan wrote. Such a ruling is "not mandated by law or regulation," he added.

But the "stay mechanism" -- triggered by the introduction of bills that are "rarely, if ever enacted" -- also could hinder ICE from "from removing aliens" who "pose a risk to public safety or national security," Homan wrote.

In that vein, Homan wrote that ICE will change its policy on private bills in four key ways:

ICE will issue a deportation stay "only if the Chair of the full Committee expressly makes a written request," not merely when a request for an investigative report is made.

ICE won't grant a beneficiary more than one stay of removal.

The duration of a stay "will be limited" to six months and possibly a one-time 90-day extension, if committee chairs request it.

If ICE finds "derogatory information" about someone after a stay is issued, the agency "will take appropriate action, including ... removal."

Undocumented for decades

Vizguerra came to the United States in 1997 from Mexico without proper documents. She arrived with her husband and eldest daughter, who now participates in the Deferred Action for Childhood Arrivals program, or DACA , which lets undocumented people brought to the country as kids attend school and work.

She landed on ICE's radar in 2009, when she was pulled over and charged with, among other minor violations, "attempted possession of a forged instrument." That involved a job application on which she used a made-up -- not stolen -- Social Security Number, Meyer has said.

Still, she was allowed to stay in the country, provided she checked in periodically with ICE. After Trump took office, Vizguerra decided to skip her scheduled check-in, and instead took sanctuary at the First Unitarian church in Denver. She eventually moved to the First Baptist Church of Denver, logging 86 days in hiding before her stay of removal was granted.

Hernandez, who is Mexican, overstayed his visitor's visa in 2003. He came to ICE's attention and was told to leave the country in 2010, when he was arrested on "local criminal charges," the agency has said, though his supporters say he has no convictions.

The father of two took refuge at the First Unitarian church in 2014, until he got a letter telling him he was no longer an "enforcement priority," he has said. He was detained again by ICE in April.

Correction: This story was updated to reflect that Vizguerra was not arrested by ICE; she voluntary skipped a mandated check-in and instead sought refuge in a church.