(CNN) -- Mexican migration to the United States may have stalled, as a new study shows, but the political and social debates over immigrants living in the United States aren't going anywhere, experts say.

The immigration debate is reflected in a number of policies and proposals, most recognizably state immigration laws that are being challenged.

Oral arguments are scheduled at the Supreme Court on Wednesday as the justices decide whether Arizona can enforce its controversial immigration law.

A bill in Mississippi that would require police to check the immigration status of all those arrested died in the state Senate this month.

Amid the backdrop of contentious debates comes a study this week from the Pew Hispanic Center, which finds that for the first time in decades, the flow of Mexican migrants to and from the United States balances out.

The effect may be even more pronounced. According to the report, "the trend lines ... suggest that return flow to Mexico probably exceeded the inflow from Mexico during the past year or two."

"The largest wave of immigration in history from a single country to the United States has come to a standstill," the report announces.

The report's findings weren't a surprise to several Mexican immigrants in Los Angeles, who said they've seen the political and economic situation shift dramatically in recent years.

"It isn't like it was before. The laws have changed. The work is very hard. Life is very expensive," said Norma Ibarra. "It's not the United States it was 30 years ago."

Alba Roche said her nieces in Mexico want to come to the United States, but can't.

"They haven't been able to come because of the situation, because there is not enough work, and more than anything because crossing is quite dangerous, so there are many obstacles," she said.

Those who study immigration trends and policy agree that the apparent standstill in immigration is significant, but to varying degrees they say it will do little to change attitudes and actions in the United States.

Jeffrey Passel, senior demographer at the Pew Hispanic Center and one of the report's authors, said that as Mexican families have fewer children, the number of potential immigrants is shrinking. Also, the Mexican economy is improving and providing jobs that before weren't available and provided a push to look for opportunities in the United States.