Cassandra Arellano, of Ellensburg, Wash., left, joins others at a rally organized by the group OneAmerica as they shout chants supporting immigration rights, education, and other issues, Wednesday, Feb. 6, 2013, at at the Capitol in Olympia, Wash. (Ted S. Warren/AP)

Immigration advocates, backed by the White House, have begun a nationwide lobbying campaign, including rallies in more than a dozen cities and a planned demonstration on the Mall.

The loosely coordinated effort is aimed in part at influencing an ongoing debate in the Republican Party over whether to provide a path to citizenship for more than 11 million illegal immigrants, organizers said.

The campaign includes liberal-leaning Hispanic, Asian and African American groups and labor unions, as well as a more centrist coalition of faith, law enforcement and business representatives. Organizers said they are intent on making their voices heard at a time when some GOP leaders have called for granting undocumented residents legal status, but have stopped short of citizenship.

The debate is one of the key points of conflict between President Obama and lawmakers, who are attempting to negotiate the largest overhaul of immigration laws in three decades.

“The election sent Republicans a strong message to work with President Obama to fix our broken system or else face political suicide,” said AFL-CIO President Richard Trumka, whose organization announced plans Thursday for 14 rallies in big cities, along with phone calls, leaflets and television ads. “Our focus is citizenship, getting people to have the same rights as anybody else.”

In recent days, an increasing number of congressional Republicans have embraced what they described as a middle ground between full citizenship and the position long held by many in the GOP that illegal immigrants be required to return to their home countries.

Some House Republicans have argued that illegal immigrants could be allowed to live and work in the United States without fear of deportation, but should not be granted the full benefits of being a citizen, including the right to vote.

“If we can find a solution that is short of pathway to citizenship but better than just kicking 12 million people out, why is that not a good solution?” Rep. Raúl R. Labrador (R-Idaho) said this week during an immigration hearing in the House Judiciary Committee.

Clarissa Martinez de Castro, an official with the National Council of La Raza, told reporters in a conference call this week that the Republican tactic creates a “false choice” between the extremes of mass deportation and immediate citizenship. In reality, she said, both Obama and a bipartisan Senate working group have advocated a fairly arduous route that would require illegal immigrants to pay back taxes and learn English, among other requirements, before some would earn citizenship.

“To try to paint that rigorous path as amnesty or as extreme is simply incorrect and frankly out of step with where the American people are,” she said.

Obama, whose reelection was powered with overwhelming support from Latino and Asian voters, has vowed not to settle for a bill that does not include a citizenship provision. At a meeting with advocates this week, he urged them to help the administration keep the pressure on Capitol Hill.

A network of activist groups led by the Service Employees International Union is planning a major rally April 10 on the West Lawn of the Capitol that organizers said could draw tens of thousands of demonstrators. Smaller events will be held across the country to build momentum leading up to that date, said Ben Monterroso, SEIU’s national field director for immigration reform.

The activists said they expect a bipartisan Senate working group to produce legislation by mid-March. That group, made up of four Democrats and four Republicans, released principles last week that included a path to citizenship.

“We’re going to be targeting specifically those people in key positions in Congress,” Monterroso said, “but we’re not letting anybody off the hook.”

Months after GOP leaders began signaling that the party would shift positions on immigration in response to their shellacking in the November election, Republicans are still working out their stance. Some Democrats and advocacy groups say that public pressure could be particularly effective at exposing divisions within the GOP.

For instance, even as a number of his House Judiciary Committee colleagues expressed wariness about the Senate plan this week, Rep. Darrell Issa (R-Calif.) said he favors the goal of citizenship.

“I don’t support amnesty for 11 million illegal aliens, especially for felons or those whose burden to our social welfare systems will outweigh their contributions,” Issa said. “But for those who we decide should be allowed to stay, we shouldn’t limit them to some secondary status that prohibits them from becoming citizens.”

The AFL-CIO says that allowing millions of undocumented residents to remain in the country without full citizenship would continue a caste system that drags down wages and health benefits for all workers. The union has rallies planned in Las Vegas, Seattle, Portland, San Francisco, Anaheim, Calif., Phoenix, Denver, Houston, Atlanta, Miami, New York and St. Paul, Minn.

Another coalition — composed of religious, law enforcement and business officials — will hold a panel discussion in Austin on Wednesday. The event will feature Barrett Duke, vice president of the Southern Baptist Ethics and Religious Liberty Commission, and Grover Norquist, president of Americans for Tax Reform, both of whom support immigration reform.

The Texas Association of Business also will take part, said Ali Noorani, executive director of the National Immigration Forum, which is coordinating the coalition that uses the motto “bibles, badges and business.”

“Look, last year the debate was over deportation or legal status,” Noorani said. “We’ve moved ahead by leaps and bounds. From our perspective, every aspiring American should be put on the road to become a citizen.”