LOS ANGELES — They pushed strollers, tugged toddlers and streamed into the convention center in the heart of this city on Sunday, thousands of immigrants here illegally and anxious to find out if they could gain protection from deportation under executive actions by President Obama.

The crowd, waiting in a long snaking line to check in, was drawn by an information session organized by advocacy groups offering people initial assessments to see if they meet the requirements to apply to stay in the country and work. The day became a kind of coming-out party for about 5,000 unauthorized immigrants, the largest gathering in the country of people who might qualify for temporary protection since the president’s announcement last month.

Delfina Ibarra, 40, from Mexico, was taking in information while nursing a 17-month-old, Kimberly, the newest citizen in the family. Ms. Ibarra, who has lived in California for 23 years, said she also has a 21-year-old son who is a citizen. She said that without documents, she has been limited to cleaning houses and packing crates in industrial distribution centers. With a legal deferral document and a work permit, Ms. Ibarra said, she could get a driver’s license and go back to school.

“It’s never too late to start again,” she said, laughing and holding up her baby.

Immigration advocates convened the information session in downtown Los Angeles not just to give out information but to galvanize their supporters as Republicans, angered by what they see as an illegal power grab by Mr. Obama, say they will seek to halt the programs when they gain control of both houses of Congress next year. Texas was joined by more than 20 other states, most led by Republicans, in filing a lawsuit to stop the president’s actions, arguing he exceeded his constitutional authority.