WASHINGTON — The Supreme Court appears to be highly skeptical of laws that try to police false statements during political campaigns, raising doubts about the viability of such laws in more than 15 states.

Justices expressed those concerns early and often Tuesday during arguments in a case challenging an Ohio law that bars people from recklessly making false statements about candidates seeking elective office.

The case has attracted widespread attention, with both liberal and conservative groups saying the law tramples on the time-honored, if dubious, tradition of political mudslinging. Critics say free speech demands wide-open debate during political campaigns, including protection for negative speech that may sometimes twist the facts.

The high court is not expected to rule directly on the constitutional issue because the current question before the justices is only a preliminary one: Can you challenge the law right away, or do you have to wait until the state finds you guilty of lying?

But the justices couldn’t resist going after the law itself, pointing out that the mere prospect of being hauled in front of state officials to explain comments made in the heat of an election has a chilling effect on speech.

“What’s the harm?” Justice Stephen Breyer asked Eric Murphy, attorney for the state of Ohio. “I can’t speak, that’s the harm.”

The case began during the 2010 election when a national anti-abortion group, the Susan B. Anthony List, planned to put up billboards accusing then-Rep. Steve Driehaus of supporting taxpayer-funded abortion because he voted for President Barack Obama’s new health care law. Driehaus, a Democrat who opposes abortion, claimed the group’s billboard ads distorted the truth and therefore violated the false speech law.

Driehaus filed a complaint with the Ohio Elections Commission, an action which prompted the billboard owner to decline posting the ads. The commission found probable cause that the ads violated the law, but Driehaus later withdrew his complaint after losing his re-election campaign. The Susan B. Anthony List then challenged the state law as unconstitutional, but a federal judge said the group didn’t have the right to sue because it hadn’t yet suffered actual harm.