CHICAGO — Tens of thousands of young illegal immigrants waited excitedly in lines as long as a mile and thronged to information sessions across the country on Wednesday, the first day that a federal immigration agency began accepting applications for deportation deferrals that include permits to work legally.

The public outpouring surprised both federal officials and immigrant advocates, who had expected an enthusiastic response to the Obama administration’s deferral program but were unprepared for the size and intensity of it. At Navy Pier here, young people began lining up on Tuesday evening for a counseling session about the program that was organized by an immigrants’ rights group.

By midmorning Wednesday, the line wound down the long pier, through a park and along an expressway, with young people holding sheafs of documents that they hoped would prove that they qualified for the program. By noon, event organizers said, 11,500 people had attended briefings, and more than 2,000 people had been turned away because there was not enough time or staff to deal with them.

“I know that out there many people are looking for the same thing as I am,” said Reyna Martinez, 19, who has lived in the United States since she was 7. “We are not alone; we stand together as a big crowd.”