The Health and Aging Committee planned a vote later Wednesday on the bill, which would then go to the House floor. The Senate would take up the measure after Thanksgiving at the earliest.
Chairman Lynn Wachtmann, a Republican from Napoleon, said he expected the panel to support the measure.
Protesters in pink T-shirts chanted "Hear us now!" as they packed the hall outside the committee's meeting. Some were staffers of Planned Parenthood. Other protesters wore shirts reading "Women are Watching."
State Sen. Nina Turner, a Cleveland Democrat, said at a news conference on the bill that Republicans in the Statehouse were ignoring the message sent by women with last week's re-election of Democratic President Barack Obama.
"It is absolutely immoral and unconscionable what the GOP is doing," Turner said. "They have not learned their lesson. They are at it again, but it is our job to teach them."
She said Planned Parenthood provides needed preventive health care to low-income women that would be jeopardized by the bill.
Wachtmann said other quality providers of women's health care have sprung up around the state and the bill would give those centers a chance at government funds.
"We have the potential of a lot bigger offering to a lot more women," he said. "This thought that the way everything is today is the best way to do it is just such an archaic thought."
Republican Senate President Tom Niehaus said his caucus is mulling the bill, as well as what action — if any — to take on another measure that would ban most abortions after the first detectable heartbeat. The so-called heartbeat bill, which has cleared the House and is stalled in the Senate, was another target of the Statehouse protesters, many of them female, on Wednesday.
NARAL Pro-Choice Ohio director Kellie Copeland said if that bill passes, the protests in Columbus will only get bigger and louder.
Asked what message on women's issues he took away as a Republican from last week's presidential election, Niehaus left that to others.
"There are a lot of pundits talking about what the election meant. What I try to stay focused on is what's important to Ohio right now, and that's jobs," he said. "I mean, what are we doing to help make Ohio the right place for people to start companies, employ people, and how do they go about getting jobs? That's where I want to keep the focus in the Senate."