For Mrs. Clinton, such speeches can do much to reinforce her liberal credentials while reassuring black voters who supported Mr. Obama that she is on their side.

In the same way, even if the lawsuits are unsuccessful, Democratic strategists say, they serve an important political purpose for Democrats by highlighting Republicans’ responsibility for the statutes that are being challenged. Democrats will also remind their base that Republicans have tried to mobilize their own core voters by warning, as Mitt Romney did in 2012, against the possibility of widespread voter fraud by Democrats.

Democrats acknowledge the political value of the lawsuits. Mrs. Clinton badly needs to turn out minority voters in numbers similar to those Mr. Obama drew in his 2012 re-election.

“I think it has been a growing trend in the last 10 years for campaigns to use litigation like this as a campaign weapon,” said Hans von Spakovsky, a Republican election law expert at the conservative Heritage Foundation. “The claims that they keep making, that this is going to depress turnout, just keep proving to be not true, and many of these issues have already been litigated.”

According to the nonpartisan Brennan Center for Justice at New York University School of Law, there are 14 states with new voter laws in place for the first time in a national race.

The lawsuits filed in Ohio and Wisconsin, like the 2014 North Carolina case, were brought by lawyers including Marc Elias, a leading Democratic lawyer on voter protection issues who represents four of the party’s national campaign committees.