Senate President Stan Rosenberg wants to revisit a state law that calls for voters to be registered 20 days prior to an election.

The American Civil Liberties Union, other advocacy groups and several affected individuals are challenging the law that requires prior voter registration. The group argue that the statute violates the constitution and leads to "the arbitrary disenfranchisement of thousands of eligible voters," for no reason other than that they missed a crucial deadline.

“The ACLU has raised an interesting point. We should be making it easier for people to vote and to engage in their communities, not harder. Since in Massachusetts we always want to make it easier for people to vote, this is worth considering," Rosenberg wrote in a statement Thursday.

Along with powerhouse Boston law firm Ropes & Gray, the groups are asking the court to strike down the law as unconstitutional and to allow the individual plaintiffs named in the suit to vote on Tuesday. The groups are urging Massachusetts to join the more than 15 other states that use modern technology to enable same-day registration.

"But in Massachusetts, our nearly three-week 'Voter Cutoff Law' continues to disenfranchise thousands of voters in every single election," Rahsaan Hall, director of the ACLU of Massachusetts' Racial Justice Program wrote in a statement.

The ACLU and cooperating groups say the state's new early voting system demonstrates that the 20-registration law is arbitrary and not needed.

A spokesman for Secretary of State WIlliam Galvin, the state's top elections official, told WGBH News the secretary's office does not comment on pending litigation. House Speaker Robert DeLeo's office had no comment.