Nationally, meanwhile, Mr. Obama is taking fire after his immigration service earlier this month deported a Mennonite pastor with American citizen children who had been living without authorization for years, but who came to agents’ attention because of a drunken driving conviction from the 1990s.

Activists said that deportation broke the rules Mr. Obama himself laid out in November, when he said he wanted to kick out “felons, not families.”

“It goes to who really are our champions. That’s disillusioning a lot of the electorate,” said Cesar Vargas, co-director of the Dream Action Coalition. “Democrats would like to make people believe that Republicans have a Latino problem. Well, Democrats are definitely facing a Latino problem that many of them aren’t even aware of.”