The law, one of three passed by states in 2011, takes effect this month, The Tennessean reported. All three were modeled on an Indiana law that has been upheld by the U.S. Supreme Court.
Critics say the laws, which require voters to present an approved form of photo identification before they cast their ballots, are aimed at suppressing the black vote. They also argue that voter fraud is a minor problem.
Opponents say they are almost finished with gathering signatures.
"There are multiple problems with our state law," Gerard Stranch, a lawyer in Nashville, said. "It's not just that it would have a disparate effect on minorities. It's setting up a poll tax."
Opponents are considering a lawsuit if the legislature does not act to repeal the law. They could get support from the federal government, which has refused to approve a similar law in South Carolina.
Duggar sisters unveil Christian dating rules in new book
Attkisson leaves CBS News, reportedly over network's 'liberal bias'