Efforts are underway in Arkansas, Iowa, Maine, Nebraska and Indiana to adopt or tighten requirements that voters show photo ID at the polls, reports The Associated Press.
There's a move in Iowa and New Hampshire to eliminate Election Day registration. New Hampshire may make it difficult for college students to vote. And Texas could shorten by several days the early voting period.
Supporters say the moves are necessary to combat voter fraud and increase public confidence in elections.
But research has shown that in-person fraud at the polls is extremely rare, says AP.
Critics of these restrictions warn that they'll hurt mostly poor people, minorities and students — all of whom tend to vote Democratic — as well as the elderly.
They fear, too, that the U.S. Justice Department under just-confirmed Attorney General Jeff Sessions will do little to intervene to protect voters.
At the same time, there are more bills around the country to make it easier to vote, according to the Brennan Center. Starting or expanding early voting and creating automatic voter registration are two popular proposals, says AP.
President Trump has claimed without evidence that as many as 5 million people voted illegally in the presidential election, saying the voter rolls include dead people, non-citizens and people registered in multiple states. He has called for an investigation.
Election experts are more concerned about the age of the country's voting systems and their vulnerability to tampering.
And a House committee voted on Tuesday to eliminate the federal commission responsible for working with states on those issues.
The Election Assistance Commission was created by Congress after the 2000 Florida recount to upgrade voting technology and provide election-related information to federal entities, state officials and election administrators.
"If we're looking at reducing the size of government this is a perfect example of something that can be eliminated," said Rep. Gregg Harper, R-Miss., chairman of the House Administration Committee, after the bill was approved on a 6-3 vote. "We don't need fluff."