Proponents of reform say they fear a delay could result in reform being pushed aside by other legislative battles, The Hill reported Saturday.
Rep. Luis Gutierrez, D-Ill., a leader in the push for reform, said about 1,000 people are deported every day, about half of whom live in families with children.
"We can't wait and wait and wait for immigration reform to get rolling," he said in an interview. "We pay a price in broken families and hardship every day."
Gutierrez said "we can make serious progress quickly" on immigration, compared to other contentious issues such as the national debt and gun control. He said congressional Democrats and Republicans "are a lot closer than people think" on immigration reform.
Other immigration leaders called Friday for the president to slow the rate at which illegal immigrants are deported.
White House press secretary Jay Carney hinted this week Obama would outline plans for comprehensive immigration reform in his State of the Union address next month.
Carney called such reforms "a very high priority of the president's."