Among the groups the White House is supporting are immigrant rights organizations and labor unions, which say their goal in holding dozens of citizenship workshops this spring is to build immigrant voting power. They want to bolster support for legislation creating a path to citizenship for undocumented immigrants, which Mr. Obama has long promised but has never been able to push through Congress. Recently naturalized immigrants, after all the effort they must make, are more likely to vote than longtime citizens.

“People who are eligible are really feeling the urgency to get out there,” said Tara Raghuveer, deputy director of the National Partnership for New Americans, a coalition that helped put on the workshop in Denver. “They are worried by the prospect that someone who is running for president has said hateful things.”

Mr. Trump says he is confident Latinos will support him, because he has employed many thousands of them over the years. “I’m just telling you that I will do really well with Hispanics,” he said in the Republican debate in Houston on Feb. 26.

But in a poll of Latino voters on Feb. 25 by The Washington Post and Univision, the Spanish language television network, 80 percent had an unfavorable view of Mr. Trump, including 72 percent with a very unfavorable view, far more than for other Republican candidates.

Hope Hicks, a spokeswoman for the Trump campaign, said, “No one will benefit more from Mr. Trump’s pro-worker immigration reforms than the millions of immigrants who already call America home.” She said his proposals include “limiting the ability of corporations to replace them with new, lower-wage workers brought in from abroad.” Polls show Hispanic workers favor raising wages instead of importing foreigners, Ms. Hicks said, adding, “That is the core moral principle that will guide immigration policy in a Trump administration.”

Many Mexicans have been content to live in the United States with their resident green cards. The naturalization fee is high, and Mexicans often underestimate their English and worry they will fail the test, said Manuel Pastor, a sociology professor at the University of Southern California who studies citizenship. Many Mexicans have family members who are undocumented, and think twice before engaging with the government, he said.