The Senate Health, Human Services and Medicaid Committee, with its chairman citing the need to review numerous amendments submitted by Republican and Democrat members, adjourned on Thursday morning without advancing the bill to a floor vote.
Chairman Dave Burke, R-Marysville, talked of the amendments needing to "mature."
The so-called "heartbeat bill" had been expected to come before the full Senate for a vote on Thursday. Republican Gov. John Kasich has promised to veto the measure.
Burke said he thinks there are amendments to the bill that could improve its standing in an inevitable court challenge. But, he said, as of Thursday morning he had not seen drafts of some of the proposed changes, and he didn't want to press forward.
"I don't want this to be Custer's last stand. Patton is what I want," Burke said, contrasting Lt. Col. George Custer's death in 1876 at the Battle of the Little Bighorn to Gen. George S. Patton's success leading American forces in World War II.
GOP leadership had planned potential veto override votes for Dec. 19. With no Senate vote on Thursday, it's uncertain when the bill could be voted on to leave time for lawmakers to return for an override vote.
The measure, which contains no exceptions for rape and incest, would forbid abortions after roughly six to seven weeks of pregnancy, when the heartbeats of fetuses generally can be first detected.
The bill makes it a fifth-degree felony, carrying up to one year in prison, for any doctor who violates the prohibition and performs an abortion.
NARAL Pro-Choice Ohio Executive Director Kellie Copeland said in a statement: "This delay is not a victory, but it is an important, positive sign. With a bill this horrific and immoral, we're very pleased to see Ohio legislators taking pause to consider the devastating consequences that would happen if abortion access was blocked across the state."
Expressing fears over its constitutionality, outgoing two-term Republican Kasich vetoed a "heartbeat bill" in late 2016 and instead signed a 20-week ban into law.
The governor has said he will veto the latest bill, as well. Abortion opponents hope an enacted Ohio heartbeat ban, sure to attract legal challenges in federal court, could land on appeal before the U.S. Supreme Court.
The addition of two conservatives to the court by Republican President Donald Trump has stoked opponent hopes the justices could overturn the landmark Roe v. Wade ruling in 1973 that upheld women's right to an abortion, but held states could impose reasonable restrictions.
Dozens of abortion-rights supporters testified against the bill, with many pointing out some women do not realize they are pregnant until after six weeks.
The bill passed the GOP-controlled House by a 60-35 vote on Nov. 15, with the 60 votes in favor constituting the minimum number needed to override Kasich's looming veto.
Twenty votes would be required in the 33-member Senate to reverse Kasich's rejection of the legislation. He would have up to 10 days the veto the measure once it reaches his desk.
If the General Assembly could not override Kasich's veto, Gov.-elect Mike DeWine, Ohio's Republican attorney general, has said he would sign a heartbeat-abortion ban into law.
Kasich has signed into law 20 abortion restrictions passed by Republican lawmakers since he took office in 2011. The number of Ohio clinics performing abortions since has dwindled from 16 to nine.
The 20,893 abortions recorded in Ohio last year represented a 1-percent increase, the first increase in five years. The number had been declining since 2012 and remains far below a peak of more than 45,000 abortions in 1982.
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