He compared the limits to other rules like the Mexico City Policy, which bars federal funding for overseas organizations that promote or perform abortions.
Sen. Patty Pansing Brooks of Lincoln, however, objected to the ban on funds for abortion providers and characterized it as a policy statement.
"What social policy is going to be in the budget next?" she said, the Lincoln Journal-Star reports. "We could talk about gambling and helmets and property taxes and environmental issues. Let's just put it all in the budget and then we don't have to have bills or committee hearings."
About $1.5 million in Title X grants goes through the Nebraska Department of Health and Human Services, aiming to provide services like well-woman exams, STD testing and treatment, HPV testing and vaccinations, and contraception. The leading grant recipient is Planned Parenthood of the Heartland, which receives about $300,000 per year, according to the Nebraska Catholic Conference.
"Whether it is direct or indirect, tax payer money should not go to abortion services," said Venzor. "The pro-life provision in the state budget simply keeps these clinics accountable and ensures that taxpayer dollars are not used for the killing of unborn life."
In January, the Omaha World-Herald said the provision would cut funding from Planned Parenthood.
Planned Parenthood of the Heartland said the money helps its clinics serve about 8,000 patients. Its clinics in Omaha and Lincoln also perform abortions.
Ricketts told CNA it was "absolutely false" to claim the funding rules would limit women's services.
"The exact same amount of dollars will be spent after we pass this bill, with this budget language in it, as was being spent before," he said. "Anybody is able to apply for those dollars."
"The clear majority of legislators want to have this Title X language in there," Ricketts said. He accused three members of the appropriations committee of voting the bill out of committee then working to undermine it.
"They're playing reckless games with the budget process. If they had a problem with this bill, they ought to not have voted for it out of committee," he said. "The legislature still has time to address this. They still have plenty of time to go back and pass this bill."
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Venzor encouraged voters and legislators in other states who want to implement similar restrictions on Title X money to contact the Nebraska Catholic Conference.
"We're all working hard across the country to defend life and advance the common good, and we should learn from each other," he said.
Kevin J. Jones is a senior staff writer with Catholic News Agency. He was a recipient of a 2014 Catholic Relief Services' Egan Journalism Fellowship.