The League of Women Voters and Rock the Vote, two groups that have long conducted voter registration drives, have largely suspended their work in Florida because of new laws in the state, as first reported by the New York Times on Wednesday. Their decision could prevent the registration of voters likely to support President Obama in a key swing state.

As a part of a wave of new voting laws passed across the country by GOP-controlled governors and state legislatures, Florida enacted a provision last year that mandates voter registration groups turn in the forms of newly-registered people within 48 hours or face fines of $50 for each late form. The laws have worried groups like the League of Women Voters, who argue they could face heavy fines for not complying with the provision.

Florida Republicans argue the provision helps make sure voter registration forms are turned in as quickly as possible.

But many of the groups who hold voting registration drives, such as Rock the Vote, target young and minority voters, and Democrats argue these new laws are simply intended to drive down registration and turnout of voters who are likely to support President Obama.

The Florida voter registration law is unique. Many states around the country instead pushed through a different kind of law over the last two years: a provision requiring voters to present photo identification to vote. Those provisions, too, could have a disproportionate impact on minority voters, who are less likely to have driver’s licenses.

Rock the Vote has already filed suit against the Florida law, and the Department of Justice is reviewing it as well.

Follow Perry Bacon Jr. on Twitter at @perrybaconjr