For Rock the Vote volunteers who roam rock concerts and college campuses looking for students to register, the typical dress code is jeans and a T-shirt.

But this year, many Rock the Vote organizers have traded their college clothes for suits and ties. That’s because they’re spending almost as much time in the courtroom fighting new restrictions on voters as they are out registering voters.

Rock the Vote is one of several dozen organizations, from civil rights groups to Latino, labor and women’s groups, that have launched a multipart campaign to push back against new registration rules for voters that have been enacted in many states. The fight over voter access has triggered state-level lobbying, ballot initiatives and lawsuits, and the issue will likely land before the Supreme Court.

Voting rights activists are responding to a wave of state laws enacted after the 2010 elections, which ushered in GOP majorities in more than two dozen state legislatures. Voting rights advocates have struggled to gain traction amid public indifference and more visible collective bargaining fights, but they are starting to win attention at the Justice Department and on Capitol Hill.

More than a half-dozen states have enacted new voter ID laws, and three passed new laws requiring voters to show proof of citizenship. Other laws restrict voter registration drives by third-party groups such as Rock the Vote and roll back early and weekend voting. South Carolina and Texas also have challenged Section 5 of the 1965 Voting Rights Act, which requires states with a history of discrimination to obtain Justice Department approval before changing their voting rules.

“The franchise, in my opinion, is under attack,” said Rep. Marcia Fudge (Ohio), one of several House and Senate Democrats who have responded with press conferences, field hearings and legislation.

Most recently, Rep. Steve Cohen (Tenn.) introduced the Voter ID Accessibility Act, which would require any state with a photo ID mandate to notify voters and offer them a free ID. “We haven’t seen much indication of voting fraud, but we have seen a lot of fraud in the mortgage business and the financial business,” Cohen said. “You wonder why they’re doing this.”

The Democratic National Committee has also pushed back with a website launched late last year. The fight over new state voting rules is the latest skirmish in an ongoing war between conservatives who allege widespread voter fraud and progressives up in arms over voter disenfranchisement.

Civil rights activists say the new rules disproportionately target minority, student and elderly voters, who tend to vote Democratic, and could bar up to 5 million voters from the polls this fall. Like many fighting the restrictions, Cohen blamed the wave of new state laws on an orchestrated campaign by the American Legislative Exchange Council, a nonprofit associated with David and Charles Koch, two businessmen well-known for funding conservative causes.

“ALEC is not part of any organized effort to suppress voters,” ALEC spokeswoman Kaitlyn Buss said. “Quite the contrary. The voter ID legislation is aimed at eliminating voter fraud. This is an issue that has broad public support, bipartisan support.”

Indeed, a December Rasmussen Reports poll found that 70 percent of likely voters think voter ID laws are a good idea. Such numbers have presented a challenge for voting rights organizers.

“Most people think that this is a no-brainer, that it’s not that difficult to get the ID or that most people have it,” said Elisabeth MacNamara, national president of the League of Women Voters. “That is a high educational hurdle that we are having to overcome.”

The league and allied organizations, including the American Civil Liberties Union, the Leadership Conference on Civil and Human Rights, and the Brennan Center for Justice at New York University’s School of Law, have fought back on several fronts.

Step one has been to lobby to block new laws at the state level. MacNamara pointed to several state wins, including a successful referendum campaign to overturn a new Maine law that had ended Election Day registration. Step two has been lawsuits in states such as Wisconsin and Florida to block restrictive laws from taking effect.

Voting rights activists also lobbied Attorney General Eric Holder, who some argued was slow to respond but who has now given two high-profile speeches in defense of voting rights and who rejected new South Carolina and Texas voter restrictions, which required his approval, as discriminatory. Voting rights organizers are now busy educating voters about the new laws and helping them obtain IDs.

“The ACLU is attacking this from every angle,” said Laura Murphy, director of the ACLU’s Washington, D.C., legislative office. “This has become a huge national priority, and we hope to have an impact.”

Amid all the lobbying and lawsuits, voting rights advocates are struggling to keep up with their normal voter registration work. Usually at this time of year, organizers are busy giving voters basic information about when and where to vote, said Marcia Johnson-Blanco, co-director of voting rights at the Lawyers’ Committee for Civil Rights Under Law.

“Now, we are finding ourselves also having to ensure that they can actually cast a ballot, make sure that they have the documents they need and educating them on how to get the documents they need,” she said.