Growing numbers of Hispanic voters in the region, themselves divided on the question of immigrant rights, also complicate the equation.
Given the finite federal resources and the new priorities, advocates worry that immigrant rights and services are at risk.
"Form a human chain in an expression of solidarity for immigrant rights," the flier read.
The group has worked for such causes as immigrant rights and death-penalty abolition.
They have often taken to the streets to rally on behalf of immigrant rights and an end to the Iraq war.
This would be a vital tactic in Chávez's future struggles in fighting for immigrant rights.
He was an outspoken advocate for reform, prohibition, immigrant rights, and international peace.
Advocates of immigrant rights contend that some guest workers should be able to apply for permanent residence.
Now, the church is active in the New Sanctuary Movement for immigrant rights.