“It has been the saddest thing for so many people who were here, and in every other way following the laws,” said Alejandro Silvestre, 36, a Guatemalan-born father of three and an owner of a strip-mall cellphone shop. “But they got grabbed and sent back to Guatemala or Mexico and their families stayed here. Sometimes their kids were raised by others. For me, thank God, that has never happened. But one is always thinking of that.”

Mr. Silvestre is among those who are hoping their lives will be transformed by Mr. Obama’s action. On Thursday evening, just before the president’s speech, he imagined the places in the United States he may soon visit without fear of being deported. “This is a great country,” he said, “but what does it matter if we are unable to travel and enjoy it?”

Other Hispanics were more skeptical. “Pura mentira” — pure lies, said José Perez, 37, a construction worker from Oaxaca, Mexico, on Thursday night. “It’s just going to be nice words. I doubt it’s going to change anything.”

The next morning, Gabriela Watson, an immigration attorney in downtown Albertville, said her phone had been ringing off the hook with clients who wanted to know when and how to apply.

She was telling them to gather their tax records, their children’s report cards, and other documents they could use to prove they had been here for five years.

“This new thing gives them hope,” she said.

But many whites said they felt stung by what they see as an audacious and unconstitutional move by a president that they never much cared for in the first place. Some worried that the action would trigger a new wave of illegal immigrants.