When immigration activists take to the streets Thursday for a series of May Day marches in downtown Los Angeles, their message will be largely directed at President Obama.

“The president needs to be pressured to use the authority that he has to keep families together,” said the Rev. David Farley, pastor at Echo Park United Methodist Church, who is helping to organize the protests.

As the window for Congress to pass an immigration overhaul bill narrows, activists are increasingly turning their attention to the president, urging him to use his executive powers to slow deportations. In actions across the country, protesters have labeled Obama “deporter in chief.”

Activists cite immigration statistics showing that deportations have risen since Obama took office. But a recent Times analysis of the statistics shows that much of that rise is attributable to a change in the way deportations are counted. In fact, immigrants living illegally in most of the continental U.S. are less likely to be deported today than before Obama came to office, according to the data.

Stephen Legomsky, a professor of immigration law who previously served in the Obama administration as chief counsel for U.S. Citizenship and Immigration Services, says activists are unfair and unwise to target Obama.

He pointed to the presidential order known as Deferred Action for Childhood Arrivals, which grants temporary legal status to immigrants who were brought to the United States as children, as proof of Obama’s efforts to bring relief to some immigrants.

“At a time when the opposing party has been relentlessly attacking the administration in the hope of gaining control of Congress, the friendly fire from those who have every reason to be supportive is not just unfair and mystifying, it is damaging,” Legomsky said.

Maria Elena Durazo, the head of the Los Angeles County Federation of Labor, which is organizing one of Thursday’s marches, says it is essential to keep the heat on Obama, who recently ordered the director of the Homeland Security Department to review the way immigration laws are handled.

“The facts on the ground are that it’s still a crisis,” Durazo said, citing members of her union who face deportation even though they did not commit serious crimes. “I think that he needs to do a lot more.”

She said the president could start by cutting back on a program that instructs local law enforcement officers to collaborate with federal immigration agents in order to identify and deport people who are in the country illegally.

Durazo said her group would also continue to put pressure on House Republicans, who have not taken up a vote on a bipartisan bill passed by the Senate last year that would lay out a path for people here illegally to apply for citizenship. Immigrant supporters have asked members of Congress to vote on the Senate bill or to craft a similar law that achieves the same thing. Republican leaders in the House have said they will take up a series of smaller bills instead, with a priority on securing the nation’s borders before any path to citizenship is granted.

Organizers of Thursday’s marches say they don’t expect the crowds to be anywhere near the size they were in 2006, when hundreds of thousands of people turned out in Los Angeles to protest proposed legislation that would have classified immigrants in the country illegally as felons.

Traditionally a day of protest for the labor movement, May Day has in recent years also become a national day of protest for immigrant rights groups. The first protest Thursday is scheduled to begin at 10 a.m. at the intersection of Cesar E. Chavez Avenue and North Broadway. Co-organized by labor and immigrant rights groups, protesters will call for an end to deportations as well as a higher minimum wage for workers.

Other immigrant groups are planning protests downtown later that day.

kate.linthicum@latimes.com