The Rev. Emma Lozano, who founded Centro Sin Fronteras in Chicago and has a long history with Mr. Obama on immigration, said they are giving the president until Thanksgiving to take unilateral action halting deportations, and then they will rally.

“We will march and run our own Latino independent candidate for president of the United States,” she said in an email announcing her plans to her network of supporters.

She is circulating a Draft Gutierrez petition form she is asking activists to bring to the polls next month in order to get signatures showing support for Mr. Gutierrez to run as an independent.