Taking up a closely watched case on the roles of truth and lies in modern politics, Supreme Court justices Tuesday appeared skeptical about the constitutionality of an Ohio law that criminalizes false statements about candidates in the days before elections.

Emphasizing the need for a ruling with midterm elections approaching, the high court heard oral arguments on the law, which bars reckless statements — lying — about candidates for political office. The decision could void similar statutes in more than a dozen other states.

At issue were billboards prepared in 2010 by the Susan B. Anthony List, a pro-life group, accusing Steven Driehaus of supporting taxpayer-funded abortions because the Democrat voted in Congress for the Affordable Care Act.

Mr. Driehaus, who lost his re-election bid, filed a complaint with the Ohio Elections Commission. The commission found “probable cause” that the pro-life group violated a state law against making false statements in the 60-day window before the election.