The measure, introduced by Republican Rep. Lamar Smith of Texas, returns power the immigration service lost under U.S. Supreme Court rulings in 2001 and 2005, El Nuevo Herald of Miami reported.
"It is an effort by Smith to get some publicity and derail the talk about immigration reform which is the real issue," said Wilfredo Allen, a prominent Miami immigration attorney.
While the Smith bill does not mention Cubans, activists in Miami said island immigrants likely would be among those most affected if the measure becomes law.
Susana Barciela of the Florida Immigrant Advocacy Center, agreed.
"This bill is so sweeping that it would result in thousands of harmless immigrants being jailed for years -- among them, asylum seekers and torture survivors," she said.
Miami immigration lawyer Ira Kurzban called the bill an "attempt to reverse" prior Supreme Court rulings.
Julio Munoz, who arrived from Cuba during the 1980 Mariel boatlift, said he spent more time in immigration detention in the United States than he did in prison for drug convictions.
"If they detain me again until I can be deported, I'd rather kill myself," Munoz said.