WASHINGTON (CNN) -- Jonathan remembers the day, several years ago, when the father of two was forced to sit his young daughter down and explain that, as an undocumented immigrant, she probably wouldn't be allowed to tour the White House with her eighth-grade class.

That day still breaks his heart.

"It's hard because what happens is your hopes begin to fade away and your future is in the short term," Jonathan said. "You're living day-by-day, not by year."

The family, who is living illegally in Florida and asked that their last names be withheld to protect their identities, is one of thousands who have the most at stake following the U.S. Supreme Court's decision to largely overturn Arizona's immigration law.

Political pundits have argued the legal merits of the case for months. But for those in the United States without documentation, those whose job prospects have been usurped by cheaper illegal labor, and the local governments forced to absorb the enormous costs associated with illegal immigration, the case goes far beyond politics.

For them, it is a daily battle between a fear of arrest and deportation and a government some feel hasn't done enough to stop illegal immigration.

The court struck down core portions of the Arizona law in a 5-3 ruling concluding, as Justice Anthony Kennedy wrote in the majority opinion, that "the national government has significant power to regulate immigration."

However, the court also upheld the provision that lets police officers enforcing other laws scrutinize the immigration status of someone if they believe that "reasonable suspicion" exists that the person is in the United States illegally.

"This is a gray day for people like me," reacted Jonathan to that provision, dubbed by critics as "show me your papers." "This basically gives the state of Florida permission to follow in Arizona's footsteps.

"Imagine the exodus of all the people who are afraid," he said. "Families will be separated."

But both Republicans and Democrats rushed to claim a limited victory.

"I am pleased that the Supreme Court has struck down key provisions of Arizona's immigration law," President Barack Obama said in a written statement Monday.

"At the same time, I remain concerned about the practical impact of the remaining provision of the Arizona law that requires local law enforcement officials to check the immigration status of anyone they even suspect to be here illegally," Obama said.

Republican leaders did not share the same opinion. "Once again we are reminded that President Obama has failed to keep his promise on immigration reform," said RNC Chairman Reince Priebus. "In the absence of presidential leadership, states have acted on their own to serve their people and enforce the law, but the issue cannot fully be resolved with a president unwilling to keep his promises. This decision makes that job even more difficult, and it leaves Americans waiting for a plan the president promised to deliver years ago."

For immigrants such as Jonathan who've spent years living in the shadows, the ruling may offer a glimmer of hope. But it also makes him feel as if life is about to get a lot more precarious.

"When all of this was happening and (Florida's) Gov. (Rick) Scott was talking about the Arizona law and how they wanted to do the same," Jonathan says, his voice breaking. "The walls were closing in on us pretty fast. We were losing hope."

Experts say, at its core, the anxiety over immigration has to do with the nation's drastically shifting racial demographics.

"Most of the vitriol and anxiety people feel about immigration has to do with one simple concept, the changing demographics of America," said CNN contributor Ruben Navarrette.

According to recent Census figures, minorities are half of the U.S. population under age 1. When these children come of age, they could help consolidate a political power base in places like Alabama, Mississippi and Georgia. That political power hold will stretch across the Southwest all the way to California, experts say. The states with the biggest increases in minority birthrates are also the states that had been considering tough laws like Arizona's.

And there are those who still see laws like the Arizona measure as a necessary step to fixing the poor job the federal government has done in resolving the immigration crisis.

"I have a cousin who is in construction. He has had to bring his prices down; he is constantly looking for work; he can't get work as a skilled laborer because he has to compete with the suppressed wages from illegal immigration," said Pauline Olvera, a former small business owner and vice chair of the Denver Republican Party. "We cannot be the only country in the world that doesn't enforce immigration laws."

She said she has watched in frustration as American citizens have been unable to get jobs.

"When illegal immigrants are here...nobody blames them for wanting to pursue the opportunity," she said. "When you have the people here illegally, the opportunity for exploitation in the workforce is higher, and it makes it difficult for American workers to compete for jobs."

Jonathan, an engineer by training, said he understands those concerns. But for him, "it feels like it is Gestapo."

He is one of the lucky ones with government-issued identification. So, he feels a bit safer. For now.

But he's prepared to flee if things take a turn. After all, it's what his close friends plan on doing.

"If I'm pulled over and I'm asked for my papers, I have a license," Jonathan said. "For our (friends), they're going to pack up and go to friendlier pastures. Friendlier states."

CNN's Bill Mears contributed to this report.