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Even as they fight with the White House, the advocacy groups are in danger of splitting with one another.

On Monday, they held separate rallies outside the White House with different messages.

United We Dream organized a midday rally with more than 100 people to pressure Mr. Obama to “go big” by taking executive action.

Minutes after that rally ended, the National Day Laborer Organizing Network had about 20 people set up a picket line outside of one of the White House entrances, demanding that other immigration advocacy groups refuse to attend meetings with Mr. Obama until he includes illegal immigrants in those sessions.

“No more meetings about us, without us,” the pickets chanted, saying the voices of illegal immigrants themselves have been ignored in the White House.

The National Day Laborer Organizing Network targeted three groups: the National Immigration Forum, the Leadership Conference on Civil Rights and the Center for American Progress, which is a liberal think tank closely associated with the White House.

Ali Noorani, executive director of the forum, posted a Twitter message saying he missed the advocates because he was at the dentist, but urged Mr. Obama to meet with them — though he stopped short of saying he would agree to their call for a boycott.

“I agree, POTUS should meet with undocumented families to understand what is at stake,” he said in one of his messages, using the acronym for “president of the United States.”

He also pointed out that Mr. Obama has met with so-called dreamers, the young adults who obtained tentative legal status under the deferred action program but are still considered to be illegal immigrants.

Overshadowing the internal fight is the distrust of Mr. Obama among immigrant advocates.

One of the advocates picketing Monday, Rosi Carrasco, said she believed Mr. Obama was intentionally trying to produce a split within the immigrant rights movement by scheduling meetings with some groups and not with others, or with illegal immigrants.

“I want to believe that the president will do the right thing,” she said. She would not say she was confident that Mr. Obama would meet her expectations on halting deportations.

She has much at stake in his decision. She came to the country 20 years ago and is in the U.S. illegally. She said she came forward after her two daughters, both of them dreamers, applied for and received tentative legal status.