"They're going to starve, they're going to be evicted and some are going to die needlessly," Conyers said Thursday in front of the Detroit state offices.
The law, which goes into effect Saturday, caps lifetime cash welfare benefits at four years, the Detroit Free Press reported.
"It's easy to say get a job, but where are the jobs?" said protester and member of the Michigan Welfare Rights Organization Gwen Gaines.
The four-year limit applies to cash assistance only and does not apply to food assistance or Medicaid, The Detroit News reported.
About 21,000 people who will lose payments are concentrated in Detroit, particularly in areas with high crime and poverty rates.
"I think it's tragic," said state Sen. Bert Johnson, D-Highland Park. "You can't have high violence and crime and poverty and expect that Detroit's going to be able to compete in its comeback."
Sara Wurfel, a spokeswoman for Gov. Rick Snyder, said benefits are being cut because "the state can no longer afford" to give cash assistance for so long.
"These benefits have always been intended as a safety net, not a long-term solution. More than 30 percent of those affected by this change have been receiving benefits 10 years or more," Wurfel said.